#### Vector Algebra - I Book Back Questions

11th Standard

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Maths

Time : 00:45:00 Hrs
Total Marks : 25
5 x 1 = 5
1. The value of $\overrightarrow{AB}+\overrightarrow{BC}+\overrightarrow{DA}+\overrightarrow{CD}$ is

(a)

$\overrightarrow{AD}$

(b)

$\overrightarrow{CA}$

(c)

$\overrightarrow{0}$

(d)

$-\overrightarrow{AD}$

2. A vector makes equal angle with the positive direction of the coordinate axes. Then each angle is equal to

(a)

$cos^{-1}({1\over 3})$

(b)

$cos^{-1}({2\over 3})$

(c)

$cos^{-1}({1\over\sqrt 3})$

(d)

$cos^{-1}({2\over\sqrt 3})$

3. The vectors $\overrightarrow{a}-\overrightarrow{b},\overrightarrow{b}-\overrightarrow{c},\overrightarrow{c}-\overrightarrow{a}$ are

(a)

parallel to each other

(b)

unit vectors

(c)

mutually perpendicular vectors

(d)

coplanar vectors.

4. If$\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$are the position vectors of three collinear points, then which of the following is true?

(a)

$\overrightarrow{a}=\overrightarrow{b}+\overrightarrow{c}$

(b)

$2\overrightarrow{a}=\overrightarrow{b}+\overrightarrow{c}$

(c)

$\overrightarrow{b}=\overrightarrow{c}+\overrightarrow{a}$

(d)

$4\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}=0$

5. If $\lambda \hat{i}+2\lambda \hat{j}+2\lambda \hat{k}$ is a unit vector, then the value of $\lambda$is

(a)

${1\over3}$

(b)

${1\over4}$

(c)

${1\over9}$

(d)

${1\over2}$

6. 3 x 2 = 6
7. Represent graphically the displacement of 80km, 60° south of west

8. Find the direction cosines of a vector whose direction ratios are 2, 3, - 6.

9. Find the direction cosines of $\overrightarrow{AB},$where A is (2, 3, 1) and B is (3, - 1, 2).

10. 3 x 3 = 9
11. Show that the points whose position vectors are 2$\hat{i}$+ 3$\hat{j}$− 5$\hat{k}$, 3$\hat{i}$+ $\hat{j}$− 2$\hat{k}$ and, 6$\hat{i}$− 5 $\hat{j}$+ 7$\hat{k}$ are collinear

12. If $\overrightarrow{a},\overrightarrow{b},$and $\overrightarrow{c}$ are three unit vectors satisfying  $\overrightarrow{a}-\sqrt{3}\overrightarrow{b}+\overrightarrow{c}=\overrightarrow{0}$  then find the angle between $\overrightarrow{a}$ and $\overrightarrow{c}$ .

13. Find the unit vector in the direction of the vector $\overrightarrow { a } -2\overrightarrow { b } +3\overrightarrow { c }$ if $\overrightarrow { a } =\hat { i } +\hat { j } ,\overrightarrow { b } =\hat { j } +\hat { k }$ and $\overrightarrow { c } =\hat { i } +\hat { k }$ .

14. 1 x 5 = 5
15. If $\overrightarrow{a},\overrightarrow{b}$are unit vectors and $\theta$ is the angle between them, show that $sin {\theta \over 2}={1\over2}|\overrightarrow{a}-\overrightarrow{b}|$