Recent questions tagged ch10

If $\mid\overrightarrow{a}\mid=4$ and $-3\leq\:\lambda\leq 2$,then the range of $\mid\lambda\overrightarrow{a}\mid$ is

asked Jan 17, 2013 by sreemathi.v

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If $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ are three vectors such that $\mid\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}\mid=0$ and $\mid\overrightarrow{a}\mid=.2, \mid\overrightarrow{b}\mid=3,\mid\overrightarrow{c}\mid=5$,then value of $\overrightarrow{a}.\overrightarrow{b}+\overrightarrow{b}.\overrightarrow{c}+\overrightarrow{c}.\overrightarrow{a}$ is

asked Jan 17, 2013 by sreemathi.v

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Projection vector of $\overrightarrow{a}$ on $\overrightarrow{b}$ is

asked Jan 17, 2013 by sreemathi.v

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If $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ are unit vectors such that$\mid\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}\mid=0$,then the value of $\overrightarrow{a}.\overrightarrow{b}+\overrightarrow{b}.\overrightarrow{c}+\overrightarrow{c}.\overrightarrow{a}$ is

asked Jan 17, 2013 by sreemathi.v

1 answer

The vector $\hat i+\lambda\hat j+\hat k,\hat i+\hat j-\hat k$ and $3\hat i+6\hat j-5\hat k$ are coplanar if

asked Jan 17, 2013 by sreemathi.v

1 answer

If $\mid\overrightarrow a\mid=10,\mid\overrightarrow b\mid=2$ and $\overrightarrow a.\overrightarrow b=12$,then value of $\mid\overrightarrow a\times\overrightarrow b\mid$ is

asked Jan 17, 2013 by sreemathi.v

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For any vector $\overrightarrow{a}$,the value of $(\overrightarrow{a}.\hat i)^2+ (\overrightarrow{a}.\hat j)^2+ (\overrightarrow{a}.\hat k)^2 $ is equal to

asked Jan 17, 2013 by sreemathi.v

1 answer

The vector from origin to the points $A$ and $B$ are $\overrightarrow{a}=2\hat i-3\hat j-2\hat k$ and $\overrightarrow{b}=2\hat i+3\hat j-\hat k,$ respectively,then the areqa of triangle $OAB$ is

asked Jan 17, 2013 by sreemathi.v

1 answer

The value of $\lambda$ for which the vectors $3\hat i+6\hat j+\hat k $ and $ 2\hat i+4\hat j+\lambda\hat k$ are parallel is

asked Jan 17, 2013 by sreemathi.v

1 answer

Find the value of $\lambda$ such that the vectors $\overrightarrow{a}=2\hat i+\lambda\hat j+\hat k$ and $\overrightarrow{b}=\hat i+2\hat j+3\hat k$ are orthogonal

asked Jan 17, 2013 by sreemathi.v

1 answer

The angle between two vectors $\overrightarrow{a}$ and $\overrightarrow{b}$ with magnitudes $\sqrt 3$ and 4,respectively,and $\overrightarrow{a}.\overrightarrow{b}=2\sqrt 3$ is

asked Jan 17, 2013 by sreemathi.v

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The vector having initial and terminal points as $(2,5,0)$ and $(-3,7,4)$ respectively is

asked Jan 17, 2013 by sreemathi.v

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The position vector of the point which divides the join of points $2\overrightarrow{a}-3\overrightarrow{b}$ and $\overrightarrow{a}+\overrightarrow{b}$ in the ratio 3:1 is

asked Jan 17, 2013 by sreemathi.v

1 answer

The vector in the direction of the vector $\hat i+2\hat j+2\hat k$ that has magnitude $9$ is

asked Jan 17, 2013 by sreemathi.v

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If $\overrightarrow{a}=\hat i+\hat j+\hat k$ and $\overrightarrow{b}=\hat j-\hat k$,find a vector $\overrightarrow{c}$ such that $\overrightarrow{a}\times\overrightarrow{c}=\overrightarrow{b}$ and $\overrightarrow{a}.\overrightarrow{c}=3$.

asked Jan 17, 2013 by sreemathi.v

1 answer

Show that the area of the parallelogram whose diagonals are given by $\overrightarrow{a}$ and $\overrightarrow{b}$ is $\frac{\mid \overrightarrow{a} \times \overrightarrow{b}\mid}{2}$.Also find the area of the parallelogram whose diagonals are $2\hat i+\hat j+\hat k$ and $\hat i+3\hat j+\hat k$.

asked Jan 17, 2013 by sreemathi.v

1 answer

If $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ represent the vertices of a triangle,then show that $\frac{1}{2}\mid\overrightarrow{b}\times\overrightarrow{c}+\overrightarrow{c}\times\overrightarrow{a}+\overrightarrow{a}\times\overrightarrow{b}\mid$ gives the vector area of the triangle .Hence deduce the condition that the three points $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ are collinear.Also find the unit vector normal to the plane of the triangle.

asked Jan 17, 2013 by sreemathi.v

1 answer

Prove that in any triangle ABC,$ cos A=\large \frac{b^2+c^2-a^2}{2bc}$,$where \overrightarrow{a},\overrightarrow{b} and \overrightarrow{c}$ are the vectors of sides BC, CA and AB respectively.

asked Jan 17, 2013 by sreemathi.v

1 answer

Using vectors,prove that the parallelogram on the same base and between the same parallels are equal in area.

asked Jan 17, 2013 by sreemathi.v

1 answer

Using vectors,find the area of the triangle ABC with vertices $A(1,2,3),B(2,-1,4)$ and $C(4,5,-1).$

asked Jan 17, 2013 by sreemathi.v

1 answer

If $A,B,C,D$ are the points with position vectors $\overrightarrow{i}+\overrightarrow{j}+\overrightarrow{k},2\overrightarrow{i}+\overrightarrow{j}+3\overrightarrow{k},2\overrightarrow{i}-3\overrightarrow{k},3\overrightarrow{i}+2\overrightarrow{i}+\overrightarrow{k},$ respectively ,find the projection of $\overrightarrow{AB}$ along $\overrightarrow{CD}.$

asked Jan 17, 2013 by sreemathi.v

1 answer

Find the sine of the angle between the vectors $\overrightarrow{a}=3\hat i+\hat j+2\hat k$ and $\overrightarrow{b}=-2\hat i+2\hat j+4\hat k.$

asked Jan 17, 2013 by sreemathi.v

1 answer

If $\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}=0,$show that $\overrightarrow{a} \times \overrightarrow{b}=\overrightarrow{b} \times \overrightarrow{c} =\overrightarrow{c} \times \overrightarrow{a}$.Interpret the result geometrically?

asked Jan 17, 2013 by sreemathi.v

1 answer

Find the angle between the vectors $2\hat i\;-\hat j\;-\hat k$ and $3\hat i\;+4\hat j\;+\hat k$.

asked Jan 17, 2013 by sreemathi.v

1 answer

FInd a vector of magnitude 6 ,which is perpendicular to both the vectors $2\hat i-\hat j+2\hat k$ and $4\hat i-\hat j+3\hat k.$

asked Jan 17, 2013 by sreemathi.v

1 answer

A vector $\overrightarrow{r}$ has magnitude 14 and direction ratios 2,3,-6.Find the direction cosines and components of $\overrightarrow{r}$,given that $\overrightarrow{r}$ makes an acute angle with x-axis.

asked Jan 17, 2013 by sreemathi.v

1 answer

A vector $\overrightarrow{r}$ is inclined at equal angles to the three axes.If the magnitude of $\overrightarrow{r}$ is $2\sqrt 3$ units,find $\overrightarrow{r}.$

asked Jan 17, 2013 by sreemathi.v

1 answer

Using vectors,find the value of k such that the points $(k,-10,3),(1,-1,3)$ and $(3,5.3)$ are collinear.

asked Jan 17, 2013 by sreemathi.v

1 answer

If $\overrightarrow{a}$ and $\overrightarrow{b}$ are the position vectors of $A$ and $B$,respectively,find the position vector of a point $C$ in $BA$ produced such that $BC=1.5BA$.

asked Jan 17, 2013 by sreemathi.v

1 answer

Find a unit vector in the direction of $\overrightarrow{PQ},$where $P$ and $Q$ have co-ordinates $(5,0,8)$ and $(3,3,2)$,respectively.

asked Jan 17, 2013 by sreemathi.v

1 answer

If $\overrightarrow{a}=\hat i-\hat j+2\hat k\;and\;\overrightarrow{b}=2\hat i-\hat j-2\hat k,$then find the unit vector in the direction of $ 6 \overrightarrow{b} $

asked Jan 17, 2013 by sreemathi.v

1 answer

Find the unit vector in the direction of sum of vectors $\overrightarrow{a}=2\hat i+\hat j+\hat k\;and\;\overrightarrow{b}=2\hat j-\hat k$

asked Jan 16, 2013 by sreemathi.v

1 answer

Represent graphically a displacement of 40 km, 30° east of north.

asked Dec 7, 2012 by thanvigandhi_1

1 answer

Classify the following measures as scalars and vectors. $(i)\;10\: kg$

asked Dec 7, 2012 by thanvigandhi_1

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Classify the following as scalar and vector quantities. $ (i)\; $time period.

asked Dec 7, 2012 by thanvigandhi_1

1 answer

In Fig 10.6 (a square), identify the following vectors. \[(i)\; Coinitial\qquad (ii)\; Equal\qquad (iii)\; Collinear\; but\; not\; equal \]

asked Dec 7, 2012 by thanvigandhi_1

1 answer

Answer the following as true or false. $\\(i)\; \overrightarrow a$ and -$\overrightarrow a$ are collinear.

asked Dec 7, 2012 by thanvigandhi_1

1 answer

Compute the magnitude of the following vectors: $(i)\;\overrightarrow a = \hat i + \hat j + \hat k$

asked Dec 6, 2012 by thanvigandhi_1

1 answer

Write two different vectors having same magnitude.

asked Dec 6, 2012 by thanvigandhi_1

1 answer

Write two different vectors having same direction.

asked Dec 6, 2012 by thanvigandhi_1

1 answer

Find the values of $x$ and $y$ so that the vectors $2\hat i + 3\hat j$ and $x\hat i + y\hat j$ are equal.

asked Dec 6, 2012 by thanvigandhi_1

1 answer

Find the scalar and vector components of the vector with initial point $(2, 1)$ and terminal point $(– 5, 7).$

asked Dec 6, 2012 by thanvigandhi_1

1 answer

Find the sum of the vectors $\overrightarrow a=\hat i − 2\hat j + \hat k, \overrightarrow b=−2\hat i + 4\hat j + 5\hat k$ and $\overrightarrow c = \hat i − 6\hat j – 7\hat k$ .

asked Dec 6, 2012 by thanvigandhi_1

1 answer

Find the unit vector in the direction of the vector $ \overrightarrow a = \hat i + \hat j + 2\hat k$ .

asked Dec 6, 2012 by thanvigandhi_1

1 answer

Find the unit vector in the direction of vector $ \overline{PQ}$, where $P$ and $Q$ are the points $(1, 2, 3)$ and $(4, 5, 6)$ respectively.

asked Dec 6, 2012 by thanvigandhi_1

1 answer

For given vectors, $ \overrightarrow a=2\hat i − \hat j + 2\hat k$ and $ \overrightarrow b=−\hat i + \hat j − \hat k$, find the unit vector in the direction of the vector $ \overrightarrow a +\overrightarrow b.$

asked Dec 6, 2012 by thanvigandhi_1

1 answer

Find a vector in the direction of vector $5\hat i − \hat j + 2\hat k$ which has magnitude $8$ units.

asked Dec 6, 2012 by thanvigandhi_1

1 answer

Show that the vectors $2\hat i − 3\hat j + 4\hat k$ and $− 4\hat i + 6\hat j − 8\hat k$ are collinear.

asked Dec 6, 2012 by thanvigandhi_1

1 answer

Find the direction cosines of the vector $\hat i + 2\hat j + 3\hat k$

asked Dec 6, 2012 by thanvigandhi_1

1 answer

Find the direction cosines of the vector joining the points $A(1, 2, –3)$ and $B(–1, –2, 1),$ directed from $A$ to $B$.

asked Dec 6, 2012 by thanvigandhi_1

1 answer

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