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Recent questions tagged sec-1

Find the area of the parallelogram determined by the sides $\overrightarrow{i}+\overrightarrow{2j}+\overrightarrow{3k}$ and $-\overrightarrow{3i}-\overrightarrow{2j}+\overrightarrow{k}$

asked Apr 5, 2013 by poojasapani_1

1 answer

Find the area of the parallelogram whose diagonals are represented by $\overrightarrow{2i}+\overrightarrow{3j}+\overrightarrow{6k}$ and $\overrightarrow{3i}-\overrightarrow{6j}+\overrightarrow{2k}$

asked Apr 5, 2013 by poojasapani_1

1 answer

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 $D(2 ,-5 ,3)$

asked Apr 5, 2013 by poojasapani_1

1 answer

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.

asked Apr 4, 2013 by poojasapani_1

1 answer

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 $\overrightarrow{a}=\pm 2(\overrightarrow{b}\times\overrightarrow{c})$

asked Apr 4, 2013 by poojasapani_1

1 answer

For any three vectors $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ show that $\overrightarrow{a}\times(\overrightarrow{b}+\overrightarrow{c})+\overrightarrow{b}\times(\overrightarrow{c}+\overrightarrow{a})+\overrightarrow{c}\times(\overrightarrow{a}+\overrightarrow{b})=\overrightarrow{0}$

asked Apr 4, 2013 by poojasapani_1

1 answer

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.

asked Apr 4, 2013 by poojasapani_1

1 answer

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 $\overrightarrow{b}$

asked Apr 4, 2013 by poojasapani_1

1 answer

Find the angle between two vectors $\overrightarrow{a} $ and $\overrightarrow{b} $ if $|\overrightarrow{a} \times \overrightarrow{b}|=\overrightarrow{a}.\overrightarrow{b}$

asked Apr 4, 2013 by poojasapani_1

1 answer

Find the vectors whose length $5$ and which are perpendicular to the vectors $\overrightarrow{a}=\overrightarrow{3i}+\overrightarrow{j}-\overrightarrow{4k}$ and $\overrightarrow{b}=\overrightarrow{6i}+\overrightarrow{5j}-\overrightarrow{2k}$

asked Apr 4, 2013 by poojasapani_1

1 answer

Find the unit vectors perpendicular to the plane containing the vectors $\overrightarrow{2i}+\overrightarrow{j}+\overrightarrow{k}$ and $\overrightarrow{i}+\overrightarrow{2j}+\overrightarrow{k}$

asked Apr 4, 2013 by poojasapani_1

1 answer

If $|\overrightarrow{a}|=3, |\overrightarrow{b}|=4$ and $\overrightarrow{a}.\overrightarrow{b}=9$ than find $|\overrightarrow{a} \times \overrightarrow{b}|$

asked Apr 4, 2013 by poojasapani_1

1 answer

Find the magnitude of $\overrightarrow{a} \times \overrightarrow{b}$ if $\overrightarrow{a}=\overrightarrow{2i}+\overrightarrow{k}, \overrightarrow{b}=\overrightarrow{i}+\overrightarrow{j}+\overrightarrow{k}$

asked Apr 4, 2013 by poojasapani_1

1 answer

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.

asked Apr 4, 2013 by poojasapani_1

1 answer

The constant forces $\overrightarrow{2i}-\overrightarrow{5j}+ \overrightarrow{6k}, -\overrightarrow{i}+\overrightarrow{2j}-\overrightarrow{k},$and $\overrightarrow{2i}+\overrightarrow{7j} $ act on a particle which is displaced from position $\overrightarrow{4i}-\overrightarrow{3j}-\overrightarrow{2k}$ to position $\overrightarrow{6i}+\overrightarrow{j}-\overrightarrow{3k}$. find the work done.

asked Apr 4, 2013 by poojasapani_1

1 answer

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.

asked Apr 4, 2013 by poojasapani_1

1 answer

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 $\overrightarrow{3i}+\overrightarrow{4j}+\overrightarrow{5k}$ .

asked Apr 4, 2013 by poojasapani_1

1 answer

Prove by the vector method , cos$(A+B)=$ cos$A$ cos$B$ - sin$A$ sin$B$

asked Apr 3, 2013 by poojasapani_1

1 answer

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.

asked Apr 3, 2013 by poojasapani_1

1 answer

Prove by vector method, The mid point of the hypotenuse of a right angled tringle is equidistant from its vertices.

asked Apr 3, 2013 by poojasapani_1

1 answer

Prove by the vector method If the diagonals of a parallelogram are equal than it is a rectangle.

asked Apr 3, 2013 by poojasapani_1

1 answer

Find the projection of $\overrightarrow{3i}+\overrightarrow{j}-\overrightarrow{k}$ on $\overrightarrow{4i}-\overrightarrow{j}+\overrightarrow{2k}$

asked Apr 3, 2013 by poojasapani_1

1 answer

Find the projection of $\overrightarrow{i}+\overrightarrow{2j}-\overrightarrow{2k}$ on $\overrightarrow{2i}-\overrightarrow{j}+ \overrightarrow{5k}$

asked Apr 3, 2013 by poojasapani_1

1 answer

Find the projection of $\overrightarrow{i}-\overrightarrow{j}$ on $z$ axis

asked Apr 3, 2013 by poojasapani_1

1 answer

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.

asked Apr 3, 2013 by poojasapani_1

1 answer

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.

asked Apr 3, 2013 by poojasapani_1

1 answer

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 $\overrightarrow{u}.\overrightarrow{v}+\overrightarrow{v}.\overrightarrow{w}+\overrightarrow{w}.\overrightarrow{u}$

asked Apr 3, 2013 by poojasapani_1

1 answer

If$|\overrightarrow{a}+\overrightarrow{b}|=60, |\overrightarrow{a}-\overrightarrow{b}|=40$ and $|\overrightarrow{b}|=46$ find$|\overrightarrow{a}|.$

asked Apr 3, 2013 by poojasapani_1

1 answer

If $\overrightarrow{a}\;,\overrightarrow{b}\;,\overrightarrow{c}$ are three mutually perpendicular unit vectors,than prove that $|\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}|=\sqrt{3}$

asked Apr 3, 2013 by poojasapani_1

1 answer

If the sum of two unit vectors is a unit vector prove that the magnitude of their difference is $\sqrt{3}$.

asked Apr 3, 2013 by poojasapani_1

1 answer

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

asked Apr 3, 2013 by poojasapani_1

1 answer

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}| $

asked Apr 3, 2013 by poojasapani_1

1 answer

If $\hat{a}$ and $\hat{b}$ are unit vectors inclined at an angle $\theta$ ,than prove that tan$\large\frac{\theta}{2}$=$\large\frac{|\hat{a}-\hat{b}|}{|\hat{a}+\hat{b}|}$

asked Apr 2, 2013 by poojasapani_1

1 answer

Show that the vector $\overrightarrow{i}+\overrightarrow{j}+\overrightarrow{k}$ is equally inclined with the coordinate axes.

asked Apr 2, 2013 by poojasapani_1

1 answer

Find the angles which the vector $\overrightarrow{i}-\overrightarrow{j}+\sqrt{2}\overrightarrow{k}$ makes with the coordinate axes.

asked Apr 2, 2013 by poojasapani_1

1 answer

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

asked Apr 2, 2013 by poojasapani_1

1 answer

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.

asked Apr 2, 2013 by poojasapani_1

1 answer

If $\overrightarrow{a} =\overrightarrow{i} + \overrightarrow{j}+\overrightarrow{2k}\; and\; \overrightarrow{b}=\overrightarrow{3i} +\overrightarrow{2j}-\overrightarrow{k}$ find $(\overrightarrow{a}+\overrightarrow{3b}) . (\overrightarrow{2a}-\overrightarrow{b})$

asked Apr 2, 2013 by poojasapani_1

1 answer

Find $ \overrightarrow{a} .\overrightarrow{b}$ when $\overrightarrow{a}=\overrightarrow{2i}+\overrightarrow{2j}-\overrightarrow{k} $ and$ \overrightarrow{b} =\overrightarrow{6i}-\overrightarrow{3j}+\overrightarrow{2k}$

asked Apr 2, 2013 by poojasapani_1

1 answer

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.

asked Apr 2, 2013 by poojasapani_1

1 answer

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$

asked Apr 2, 2013 by poojasapani_1

1 answer

Examine the consistency of the following system of equation. If it is consistent than solve the same. $x+y-z=1\;,2x+2y-2z=2\;,-3x-3y+3z=-3$

asked Mar 30, 2013 by poojasapani_1

1 answer

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 $

asked Mar 30, 2013 by poojasapani_1

1 answer

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 $

asked Mar 30, 2013 by poojasapani_1

1 answer

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 $

asked Mar 30, 2013 by poojasapani_1

1 answer

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 $

asked Mar 30, 2013 by poojasapani_1

1 answer

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.

asked Mar 29, 2013 by poojasapani_1

1 answer

Solve the following non-homogeneous system of linear equation by determinant method: $\large \frac{1}{x}+\frac{2}{y}-\frac{1}{z}=1\;;\frac{2}{x}+\frac{4}{y}+\frac{1}{z}=5\;;\frac{3}{x}-\frac{2}{y}-\frac{2}{z}=0$

asked Mar 29, 2013 by poojasapani_1

1 answer

Solve the following non-homogeneous system of linear equation by determinant method : $ 2x-y+z=2\;,6x-3y+3z=6\;,4x-2y+2z=4$

asked Mar 29, 2013 by poojasapani_1

1 answer

Solve the following non-homogeneous system of linear equation by determinant method : $x+2y+z=6\;,3x+3y-z=3\;,2x+y-2z=-3 $

asked Mar 29, 2013 by poojasapani_1

1 answer

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