Class 12 vectors multiple choice question

Multiple choice (Vectors)

vectors multiple choice

Choose and write the correct option in the following question.(vectors multiple choice)

1.) The value of the expression |\vec{a}\times \vec{b}|^2=(\vec{a}.\vec{b})^2 is

(a) \vec{a}.\vec{b}            (b) |\vec{a}||\vec{b}|

(c) |\vec{a}^2||\vec{b}|^2     (d) (\vec{a}.\vec{b})

Answer (c)

2.) The area of the triangle formed by vertices O, A, B where \vec{OA} = \hat{i}+2\hat{j}+3\hat{k} and \vec{OB}= -3\hat{i}-2\hat{j}+\hat{k} is

(a) 3\sqrt{5} sq.units           (b) 5\sqrt{5} sq.units

(c) 6\sqrt{5} sq.units            (d) 4 sq.units

Answer (a)

3.) If θ is the angle between two vectors \vec{a} and \vec{b} then \vec{a}.\vec{b} \geq 0 only when

(a) 0 <\theta<\frac{\pi}{2}      (b) 0\leq \theta \leq \frac{\pi}{2}

(c) 0 < \theta <\pi                      (d) 0 \leq \theta \leq \pi

Answer (b)

4.) If θ is the angle between any two vectors \vec{a} and \vec{b} then |\vec{a}-\vec{b}|=|\vec{a}\times \vec{b}|, where θ is equal to

(a) 0                          (b) π/4

(c) π/2                       (d) π

Answer (c)

5.) The vector of the direction of the vector \hat{i}-2\hat{j}+2\hat{k} that has magnitude 9 is

(a) \hat{i}-2\hat{j}+2\hat{k}

(b) \frac{\hat{i}-2\hat{j}+2\hat{k}}{3}

(c) 3(\hat{i}-2\hat{j}+2\hat{k})

(d) 9(\hat{i}-2\hat{j}+2\hat{k})

Answer (c)

6.) The position vector of the point which divides the joining of points 2\vec{a}-3\vec{b} and \vec{a}+\vec{b} in the ratio 3:1 is

(a) \frac{3\vec{a}-2\vec{b}}{2}

(b) \frac{7\vec{a}-8\vec{b}}{4}

(c) \frac{3\vec{a}}{4}

(d) \frac{5\vec{a}}{4}

Answer (d)

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

(a) -\hat{i}+12\hat{j}+4\hat{k}

(b) 5\hat{i}+2\hat{j}-4\hat{k}

(c) -5\hat{i}+2\hat{j}+2\hat{k}

(d) \hat{i}+\hat{j}+\hat{k}

Answer (c)

8.) The angle between two vectors \vec{a} and \vec{b} with magnitude √3 and 4 respectively and \vec{a}.\vec{b}=2\sqrt{3} is

(a) π/6                   (b) π/3

(c) π/2                   (d) 5π/8

Answer (b)

9.)  The value of λ such that the vectors \vec{a} = 2\hat{i} + \lambda\hat{j}+\hat{k} and \vec{b} = \hat{i}+2\hat{j}+3\hat{k} are ortogonal is

(a) 0                     (b) 1

(c) 3/2                  (d) -5/2

Answer (d)

10.) The value of λ 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

(a) 2/3                  (b) 3/2

(c) 5/2                   (d) 2/5

Answer (a)

11.) The vectors from origin to the points A and B are \vec{a}=2\hat{i}-3\hat{j}+2\hat{k} and \vec{b} = 2\hat{i}+3\hat{j}+\hat{k}.respectively then the area of triangle OAB is

(a) 340                  (b) √25

(c) √(229)              (d) 1/2√(229)

Answer (d) 

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

(a) \vec{a}^2        (b) 3\vec{a}^2

(c) 4\vec{a}^2      (d) 2\vec{a}^2

Answer (d)

13.) If |\vec{a}| = 10,|\vec{b}| = 2 and \vec{a}.\vec{b} = 12, then value of |\vec{a}\times \vec{b}| is

(a) 5                        (b) 10

(c) 14                       (d) 16

Answer (d)

14.) The projection of vector \hat{i}-2\hat{j}+\hat{k} on the vector 4\hat{i}-4\hat{j} +7\hat{k} is

(a) \frac{5\sqrt{6}}{10}        (b) \frac{19}{9}

(c) \frac{9}{19}                   (d) \frac{\sqrt{6}}{19}

Answer (b)

15.) If \vec{a},\vec{b},\vec{c} are unit vectors such that \vec{a}+\vec{b}+\vec{c} = 0, then the value of  \vec{a}.\vec{b}+\vec{b}.\vec{c}+\vec{c}.\vec{a} is 

(a) I                         (b) 3

(c) -3/2                   (d) None of these

Answer (c)

16.) Projection vector of \vec{a} on \vec{b} is

(a) \left(\frac{|\vec{a}.\vec{b}|}{|\vec{b}|^2}\right)\vec{b}

(b) \frac{\vec{a}.\vec{b}}{|\vec{b}|}

(c) \frac{\vec{a}.\vec{b}}{|\vec{a}|}(d)

(d) \left(\frac{\vec{a}.\vec{b}}{|\vec{b}|^2}\right)\vec{b}

Answer (a)

17.) If \vec{a},\vec{b} and \vec{c} are three vectors such that \vec{a}+\vec{b}+\vec{c}=0 and |\vec{a}|=2,|\vec{b}| = 3, |\vec{c}| = 5 then value of \vec{a}.\vec{b}+\vec{b}.\vec{c}+\vec{c}.\vec{a} is

(a) 0                 (b) 1

(c) -19               (d) 38

Answer (c)

18.) If |\vec{a}| = 4  and -3 ≤ λ ≤ 2, then the range of |\lambda\hat{a}| is

(a) [0, 8]             (b) [-12, 8]

(c) [0, 12]             (d) [8, 12]

Answer (c)

19.) The number of vectors of unit length perpendicular to the vectors \vec{a} = 2\hat{i}+\hat{j}+21\hat{k} and \vec{b} = \hat{j}+\hat{k} is 

(a) one                 (b) two

(c) three               (d) Infinite

Answer (b)

20.) The position vector of the point which divides the jpin of points with position vectors \vec{a}+\vec{b} and 2\vec{a} - \vec{b} in the ratio 1:2 is

(a)  \frac{3\vec{a} +2\vec{b}}{3}

(b) \vec{b}

(d) \frac{5\vec{a}-\vec{b}}{3}

(d) \frac{4\vec{a}+\vec{b}}{3}

Answer (d)


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