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Answers posted by thanvigandhi_1

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Find the area of the parallelogram determined by the sides $\overrightarrow{i}+\overrightarrow{2j}+\overrightarrow{3k}$ and $-\overrightarrow{3i}-\overrightarrow{2j}+\overrightarrow{k}$
answered Jun 6, 2013
Toolbox:The area of a parallelogram whose sides are $ \overrightarrow a \: and \overrightarrow b \: ...
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Find the area of the parallelogram whose diagonals are represented by $\overrightarrow{2i}+\overrightarrow{3j}+\overrightarrow{6k}$ and $\overrightarrow{3i}-\overrightarrow{6j}+\overrightarrow{2k}$
answered Jun 5, 2013
Toolbox: The area of a quadilateral ABCD is $ \large\frac{1}{2} | \overrightarrow {AC} \times \overr...
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Find the area of parallelogram $A\;B\;C\;D$ whose vertices are $A(-5 ,2 ,5),B(-3 ,6 ,7),C(4 ,-1 ,5)$ and $D(2 ,-5 ,3)$
answered Jun 5, 2013
Toolbox:The area of a quadilateral ABCD is $ \large\frac{1}{2} | \overrightarrow {AC} \times \overri...
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If $\overrightarrow{a}\times \overrightarrow{b}= \overrightarrow{C}\times \overrightarrow{d}$ and $\overrightarrow{a}\times \overrightarrow{c}=\overrightarrow{b}\times\overrightarrow{d},$ show that $\overrightarrow{a}- \overrightarrow{d}$ and $\overrightarrow{b}-\overrightarrow{c}$ are parallel.
answered Jun 5, 2013
Toolbox: $ \overrightarrow a \times \overrightarrow b = -(\overrightarrow b \times \overrightarrow a...
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Let $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ be unit vectors such that $\overrightarrow{a}.\overrightarrow{b}=\overrightarrow{a}.\overrightarrow{c}=0$ and the angle between $\overrightarrow{b}$ and $\overrightarrow{c}$ is $\Large\frac{\pi}{6}.$ Prove that $\overrightarrow{a}=\pm 2(\overrightarrow{b}\times\overrightarrow{c})$
answered Jun 5, 2013
Toolbox: $ \overrightarrow a.\overrightarrow b=| \overrightarrow a|| \overrightarrow b| \cos \theta$...
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For any three vectors $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ show that $\overrightarrow{a}\times(\overrightarrow{b}+\overrightarrow{c})+\overrightarrow{b}\times(\overrightarrow{c}+\overrightarrow{a})+\overrightarrow{c}\times(\overrightarrow{a}+\overrightarrow{b})=\overrightarrow{0}$
answered Jun 5, 2013
Toolbox:$ \overrightarrow a \times \overrightarrow b = -(\overrightarrow b \times \overrightarrow a)...
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If $\overrightarrow{a}=\overrightarrow{i}+\overrightarrow{3j}-\overrightarrow{2k}$ and $\overrightarrow{b}=\overrightarrow{-i}+\overrightarrow{3k}$ than find $\overrightarrow{a}\times\overrightarrow{b}$. Verify that $\overrightarrow{a}$ and $\overrightarrow{b}$ are perpendicular to$\overrightarrow{a}\times\overrightarrow{b}$ separately.
answered Jun 5, 2013
Toolbox:$ \overrightarrow a.\overrightarrow b=| \overrightarrow a|| \overrightarrow b| \cos \theta$ ...
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If $|\overrightarrow{a}|=2, |\overrightarrow{b}|=7$ and $\overrightarrow{a}\times\overrightarrow{b}=\overrightarrow{3i}-\overrightarrow{2j}+\overrightarrow{6k}$ find the angle between $\overrightarrow{a}$ and $\overrightarrow{b}$
answered Jun 5, 2013
Toolbox: For two vectors $ \overrightarrow a \: and \: \overrightarrow b$, the vector product $ \ove...
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Find the angle between two vectors $\overrightarrow{a} $ and $\overrightarrow{b} $ if $|\overrightarrow{a} \times \overrightarrow{b}|=\overrightarrow{a}.\overrightarrow{b}$
answered Jun 5, 2013
Toolbox: $ \overrightarrow a.\overrightarrow b=| \overrightarrow a|| \overrightarrow b| \cos \theta$...
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Find the vectors whose length $5$ and which are perpendicular to the vectors $\overrightarrow{a}=\overrightarrow{3i}+\overrightarrow{j}-\overrightarrow{4k}$ and $\overrightarrow{b}=\overrightarrow{6i}+\overrightarrow{5j}-\overrightarrow{2k}$
answered Jun 5, 2013
Toolbox: For two vectors $ \overrightarrow a \: and \: \overrightarrow b$, the vector prod...
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Find the unit vectors perpendicular to the plane containing the vectors $\overrightarrow{2i}+\overrightarrow{j}+\overrightarrow{k}$ and $\overrightarrow{i}+\overrightarrow{2j}+\overrightarrow{k}$
answered Jun 5, 2013
Toolbox:For two vectors $ \overrightarrow a \: and \: \overrightarrow b$, the vector product $ \over...
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If $|\overrightarrow{a}|=3, |\overrightarrow{b}|=4$ and $\overrightarrow{a}.\overrightarrow{b}=9$ than find $|\overrightarrow{a} \times \overrightarrow{b}|$
answered Jun 5, 2013
Toolbox: $ \overrightarrow a.\overrightarrow b=| \overrightarrow a|| \overrightarrow b| \c...
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Find the magnitude of $\overrightarrow{a} \times \overrightarrow{b}$ if $\overrightarrow{a}=\overrightarrow{2i}+\overrightarrow{k}, \overrightarrow{b}=\overrightarrow{i}+\overrightarrow{j}+\overrightarrow{k}$
answered Jun 5, 2013
Toolbox: If $ \overrightarrow a = a_1\overrightarrow i+a_2\overrightarrow j+a_3\overrightarrow k, \:...
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Forces of magnitudes $3$ and $4$ units acting in the directions $\overrightarrow{6i}+ \overrightarrow{2j} +\overrightarrow{3k}$ and $\overrightarrow{3i}-\overrightarrow{2j}+\overrightarrow{6k}$ respectively act on a particle which is displaced from the point $(2,2,-1)$to$( 4,3,1)$. find the work done by the forces.
answered Jun 4, 2013
Toolbox:If a number of forces $ \overrightarrow F_1, \overrightarrow F_2, \overrightarrow F_3, ....$...
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A force magnitude $5$ units acting parallel to $\overrightarrow{2i}-\overrightarrow{2j}+ \overrightarrow{k}$ displaces the point of application from $(1,2,3)$to $(5,3,7) $ find the work done.
answered Jun 4, 2013
Toolbox:The work done by a force $ \overrightarrow F$ in displacing a particle through $ \overrighta...
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Find the work done by the force $f=\overrightarrow{2i} + \overrightarrow{j}+\overrightarrow{k}$ acting on particle, if the particle is displaced from the point with position vector $\overrightarrow{2i}+ \overrightarrow{2j}+ \overrightarrow{2k}$ to the point with the position vector $\overrightarrow{3i}+\overrightarrow{4j}+\overrightarrow{5k}$ .
answered Jun 4, 2013
Toolbox:The work done by a force $ \overrightarrow F$ in displacing a particle through $ \overrighta...
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Prove by the vector method , cos$(A+B)=$ cos$A$ cos$B$ - sin$A$ sin$B$
answered Jun 4, 2013
Toolbox: $ \overrightarrow a.\overrightarrow b=|\overrightarrow a||\overrightarrow b | \co...
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Prove by vector method , The sum of the squares of the diagonals of a parallelogram is equal to the sum of the squares of the sides.
answered Jun 4, 2013
Toolbox: For any two vectors $ \hat a \: and \: \hat b$ $(\hat a + \hat b)^2=(\hat a)^2+2\hat a.\h...
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Prove by vector method, The mid point of the hypotenuse of a right angled tringle is equidistant from its vertices.
answered Jun 4, 2013
Toolbox: If $ \overrightarrow a \perp \overrightarrow b$ then $ \overrightarrow a.\overrightarrow b=...
0 votes
Prove by the vector method If the diagonals of a parallelogram are equal than it is a rectangle.
answered Jun 4, 2013
Toolbox: If $ \overrightarrow a \perp \overrightarrow b$ then $ \overrightarrow a.\overrig...
0 votes
For what valus of $k$, the system of equations $kx+y+z=1\;,x+ky+z=1\;,x+y+kz=1\;,$have (i) unique solution (ii) more than one solution (iii) no solution.
answered Jun 3, 2013
Toolbox:Step 1The matrix equation is $ \begin{bmatrix} k & 1 & 1 \\ 1 & k &...
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Discuss the solutions of the system of equations for all values of $\lambda$. $ x+y+z=2\;,2x+y-2z=2\;,\lambda\;x+y+4z=2$
answered Jun 3, 2013
Toolbox:Step 1The matrix equation is $ \begin{bmatrix} 1 & 1 & 1 \\ 2 & 1 &...
0 votes
Examine the consistency of the following system of equation. If it is consistent than solve the same. $x+y-z=1\;,2x+2y-2z=2\;,-3x-3y+3z=-3$
answered Jun 3, 2013
Toolbox:Step 1The matrix equation is $ \begin{bmatrix} 1 & 1 & -1 \\ 2 & 2 &...
0 votes
A small seminar hall can hold 100 chairs.Three different colours(red,blue and green) of chairs are available. The cost of a red chair is Rs.240, cost of a blue chair is Rs.260, and the cost of a green chair is Rs.300. The total cost of chair is Rs.25,000. Find atleast 3 different solution of the number of chairs in each colour to be purchased.
answered Jun 3, 2013
Toolbox: Consistency of a system of 2 ( or 3 ) linear equations in 2 ( or 3 ) unknowns. Ca...
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If$A=\begin{bmatrix} 5 & 2 \\7 & 3 \end{bmatrix}$and$B=\begin{bmatrix} 2 & -1 \\-1 & 1 \end{bmatrix}$ verify that\((AB)^{T}=B^{T}A^{T}\)
answered Jun 3, 2013
Toolbox: Let $ A = [ a_{ij} ] $ be a square matrix x. Let $ A_{ij}$ be the cofactor of $ a_{ij}$. Th...
0 votes
Find the projection of $\overrightarrow{3i}+\overrightarrow{j}-\overrightarrow{k}$ on $\overrightarrow{4i}-\overrightarrow{j}+\overrightarrow{2k}$
answered Jun 3, 2013
Toolbox: For any two vectors $ \overrightarrow a \: and \overrightarrow b$, the projection of $\over...
0 votes
Find the projection of $\overrightarrow{i}+\overrightarrow{2j}-\overrightarrow{2k}$ on $\overrightarrow{2i}-\overrightarrow{j}+ \overrightarrow{5k}$
answered Jun 3, 2013
Toolbox: For any two vectors $ \overrightarrow a \: and \overrightarrow b$, the projection of $\over...
0 votes
Find the projection of $\overrightarrow{i}-\overrightarrow{j}$ on $z$ axis
answered Jun 2, 2013
Toolbox:For any two vectors $ \overrightarrow a \: and \overrightarrow b$, the projection of $\overr...
0 votes
Show that the points whose position vectors $\overrightarrow{4i}-\overrightarrow{3j}+\overrightarrow{k}, \overrightarrow{2i}-\overrightarrow{4j}+\overrightarrow{5k} ,\overrightarrow{i}-\overrightarrow{j}$ form a right angled tringle.
answered Jun 2, 2013
Toolbox: By $ \Delta$ law of vectors if $ \overrightarrow a+\overrightarrow b=\overrightar...
0 votes
Show that the vectors $\overrightarrow{3i}-\overrightarrow{2j}+\overrightarrow{k},\overrightarrow{i}-\overrightarrow{3j}+\overrightarrow{5k}$ and $\overrightarrow{2i}+\overrightarrow{j}-\overrightarrow{4k}$ form a right angled tringle.
answered Jun 2, 2013
Toolbox: By $ \Delta$ law of vectors if $ \overrightarrow a+\overrightarrow b=\overrightar...
0 votes
Let $\overrightarrow{u},\overrightarrow{v}$ and $\overrightarrow{w}$ be vector such that $\overrightarrow{u}+\overrightarrow{v}+\overrightarrow{w}=\overrightarrow{0}.$ If $|\overrightarrow{u}|=3, |\overrightarrow{v}|=4$ and $|\overrightarrow{w}|=5$ than find $\overrightarrow{u}.\overrightarrow{v}+\overrightarrow{v}.\overrightarrow{w}+\overrightarrow{w}.\overrightarrow{u}$
answered Jun 2, 2013
Toolbox: For any two vectors $ \hat a \: and \: \hat b$ $(\hat a + \hat b)^2=(\hat a)^2+2\...
0 votes
If$|\overrightarrow{a}+\overrightarrow{b}|=60, |\overrightarrow{a}-\overrightarrow{b}|=40$ and $|\overrightarrow{b}|=46$ find$|\overrightarrow{a}|.$
answered Jun 1, 2013
Toolbox: For any two vectors $ \hat a \: and \: \hat b$ $(\hat a + \hat b)^2=(\hat a)^2+2\...
0 votes
If $\overrightarrow{a}\;,\overrightarrow{b}\;,\overrightarrow{c}$ are three mutually perpendicular unit vectors,than prove that $|\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}|=\sqrt{3}$
answered Jun 1, 2013
Toolbox: For any two vectors $ \hat a \: and \: \hat b$ $(\hat a + \hat b)^2=(\hat a)^2+2\...
0 votes
If the sum of two unit vectors is a unit vector prove that the magnitude of their difference is $\sqrt{3}$.
answered Jun 1, 2013
Toolbox: For any two vectors $ \hat a \: and \: \hat b$ $(\hat a + \hat b)^2=(\hat a)^2+2\hat a.\h...
0 votes
Find the value of $m$ for which the vectors $\overrightarrow{a}=\overrightarrow{3i}+\overrightarrow{2j}+\overrightarrow{9k}$ and $\overrightarrow{b}=\overrightarrow{i}+\overrightarrow{mj}+\overrightarrow{3k}$ are perpendicular
answered Jun 1, 2013
Toolbox: If $ \overrightarrow a = a_1\overrightarrow i + a_2 \overrightarrow j+a_3 \overri...
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If $\hat{a}$ and $\hat{b}$ are unit vectors inclined at an angle $\theta$ ,than prove that cos$\Large\frac{\theta}{2}$=$\Large\frac{1}{2}$$|\hat{a}$+$\hat{b}| $
answered Jun 1, 2013
Toolbox: For any two vectors $ \hat a \: and \: \hat b$ $(\hat a + \hat b)^2=(\hat a)^2+2\hat a.\h...
0 votes
If $\hat{a}$ and $\hat{b}$ are unit vectors inclined at an angle $\theta$ ,than prove that tan$\large\frac{\theta}{2}$=$\large\frac{|\hat{a}-\hat{b}|}{|\hat{a}+\hat{b}|}$
answered Jun 1, 2013
Toolbox:For any two vectors $ \hat a \: and \: \hat b$ $(\hat a + \hat b)^2=(\hat a)^2+2\hat a.\ha...
0 votes
Show that the vector $\overrightarrow{i}+\overrightarrow{j}+\overrightarrow{k}$ is equally inclined with the coordinate axes.
answered May 31, 2013
Toolbox: If $ \overrightarrow a = a_1\overrightarrow i+a_2\overrightarrow j+a_3\overrightarrow k$ t...
0 votes
Find the angles which the vector $\overrightarrow{i}-\overrightarrow{j}+\sqrt{2}\overrightarrow{k}$ makes with the coordinate axes.
answered May 31, 2013
Toolbox: If $ \overrightarrow a = a_1\overrightarrow i+a_2\overrightarrow j+a_3\overrighta...
0 votes
Find the value of $m$ for which the vectors $\overrightarrow{a}=\overrightarrow{3i}+\overrightarrow{2j}+\overrightarrow{9k}$ and $\overrightarrow{b}=\overrightarrow{i}+\overrightarrow{mj}+\overrightarrow{3k}$ are parallel
answered May 31, 2013
Toolbox: If $ \overrightarrow a = a_1\overrightarrow i + a_2 \overrightarrow j+a_3 \overrightarrow k...
0 votes
Find $\lambda $ so that the vectors $\overrightarrow{2i}+\overrightarrow{\lambda\;j}+\overrightarrow{k}$ and $\overrightarrow{i}- \overrightarrow{2j} +\overrightarrow{k}$ are perpendicular to each other.
answered May 31, 2013
Toolbox:If $ \overrightarrow a = a_1\overrightarrow i + a_2 \overrightarrow j+a_3 \overrightarrow k,...
0 votes
Find $ \overrightarrow{a} .\overrightarrow{b}$ when $\overrightarrow{a}=\overrightarrow{2i}+\overrightarrow{2j}-\overrightarrow{k} $ and$ \overrightarrow{b} =\overrightarrow{6i}-\overrightarrow{3j}+\overrightarrow{2k}$
answered May 31, 2013
Toolbox:If $ \overrightarrow a = a_1\overrightarrow i + a_2 \overrightarrow j+a_3 \overrightarrow k,...
0 votes
If $\overrightarrow{a} =\overrightarrow{i} + \overrightarrow{j}+\overrightarrow{2k}\; and\; \overrightarrow{b}=\overrightarrow{3i} +\overrightarrow{2j}-\overrightarrow{k}$ find $(\overrightarrow{a}+\overrightarrow{3b}) . (\overrightarrow{2a}-\overrightarrow{b})$
answered May 31, 2013
Toolbox:If $ \overrightarrow a = a_1\overrightarrow i + a_2 \overrightarrow j+a_3 \overrightarrow k,...
0 votes
Examine the consistency of the following system of equation. If it is consistent than solve the same. $x-4y+7z=14\;,3x+8y-2z=13\;,7x-8y+26z=5 $
answered May 30, 2013
Toolbox: Rank method for finding consistency of a system of $m$ equation in $n$ unknowns :...
0 votes
Examine the consistency of the following system of equation. If it is consistent than solve the same. $x+y+z=7\;,x+2y+3z=18\;,y+2z=6 $
answered May 30, 2013
Toolbox: Rank method for finding consistency of a system of $m$ equation in $n$ unknowns :...
0 votes
Examine the consistency of the following system of equation. If it is consistent than solve the same. $x-3y-8z=-10\;,3x+y-4z=0\;,2x+5y+6z-13=0 $
answered May 30, 2013
Toolbox: Rank method for finding consistency of a system of $m$ equation in $n$ unknowns :...
0 votes
Examine the consistency of the following system of equation. If it is consistent than solve the same. $4x+3y+6z=25\;,x+5y+7z=13\;,2x+9y+z=1 $
answered May 29, 2013
Toolbox: Rank method for finding consistency of a system of $m$ equation in $n$ unknowns :...
0 votes
Solve the following non-homogeneous system of linear equation by determinant method: $\large \frac{1}{x}+\frac{2}{y}-\frac{1}{z}=1\;;\frac{2}{x}+\frac{4}{y}+\frac{1}{z}=5\;;\frac{3}{x}-\frac{2}{y}-\frac{2}{z}=0$
answered May 28, 2013
Toolbox: Consistency of a system of 2 ( or 3 ) linear equations in 2 ( or 3 ) unknowns. Ca...
0 votes
Solve the following non-homogeneous system of linear equation by determinant method : $ 2x-y+z=2\;,6x-3y+3z=6\;,4x-2y+2z=4$
answered May 28, 2013
Toolbox: Consistency of a system of 2 ( or 3 ) linear equations in 2 ( or 3 ) unknowns. Ca...
0 votes
Solve the following non-homogeneous system of linear equation by determinant method : $x+2y+z=6\;,3x+3y-z=3\;,2x+y-2z=-3 $
answered May 28, 2013
Toolbox: Consistency of a system of 2 ( or 3 ) linear equations in 2 ( or 3 ) unknowns. Ca...
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