# Multiple choice (Vectors)

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

1.) The value of the expression is

(a) Â  Â  Â  Â  Â  Â  (b)

(c) Â  Â  Â (d)

2.) The area of the triangle formed by vertices O, A, B where and is

(a) sq.unitsÂ  Â  Â  Â  Â  Â (b) sq.units

(c) sq.unitsÂ  Â  Â  Â  Â  Â  (d) 4 sq.units

3.) If Î¸ is the angle between two vectors and then only when

(a) Â  Â  Â  (b)

(c) Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  (d)

4.) If Î¸ is the angle between any two vectors and then , where Î¸ is equal to

(a) 0Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  (b) Ï€/4

(c) Ï€/2Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â (d) Ï€

5.) The vector of the direction of the vector that has magnitude 9 is

(a)

(b)

(c)

(d)

6.) The position vector of the point which divides the joining of points and in the ratio 3:1 is

(a)

(b)

(c)

(d)

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

(a)

(b)

(c)

(d)

8.) The angle between two vectors and with magnitude âˆš3 and 4 respectively and is

(a) Ï€/6Â  Â  Â  Â  Â  Â  Â  Â  Â  Â (b) Ï€/3

(c) Ï€/2Â  Â  Â  Â  Â  Â  Â  Â  Â  Â (d) 5Ï€/8

9.)Â  The value of Î» such that the vectors and are ortogonal is

(a) 0Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â (b) 1

(c) 3/2Â  Â  Â  Â  Â  Â  Â  Â  Â  (d) -5/2

10.) The value of Î» for which the vectors and are parallel is

(a) 2/3Â  Â  Â  Â  Â  Â  Â  Â  Â  (b) 3/2

(c) 5/2Â  Â  Â  Â  Â  Â  Â  Â  Â  Â (d) 2/5

11.) The vectors from origin to the points A and B are and .respectively then the area of triangle OAB is

(a) 340Â  Â  Â  Â  Â  Â  Â  Â  Â  (b) âˆš25

(c) âˆš(229)Â  Â  Â  Â  Â  Â  Â  (d) 1/2âˆš(229)

12.) For any vector , the value of is equal to

(a) Â  Â  Â  Â  (b)

(c) Â  Â  Â  (d)

13.) If and , then value of is

(a) 5Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  (b) 10

(c) 14Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â (d) 16

14.) The projection of vector on the vector is

(a) Â  Â  Â  Â  (b)

(c) Â  Â  Â  Â  Â  Â  Â  Â  Â  Â (d)

15.) If are unit vectors such that , then the value ofÂ  isÂ

(a) IÂ  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â (b) 3

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

16.) Projection vector of on is

(a)

(b)

(c) (d)

(d)

17.) If and are three vectors such that and then value of is

(a) 0Â  Â  Â  Â  Â  Â  Â  Â  Â (b) 1

(c) -19Â  Â  Â  Â  Â  Â  Â  Â (d) 38

18.) If Â  and -3 â‰¤ Î» â‰¤ 2, then the range of is

(a) [0, 8]Â  Â  Â  Â  Â  Â  Â (b) [-12, 8]

(c) [0, 12]Â  Â  Â  Â  Â  Â  Â (d) [8, 12]

19.) The number of vectors of unit length perpendicular to the vectors and isÂ

(a) oneÂ  Â  Â  Â  Â  Â  Â  Â  Â (b) two

(c) threeÂ  Â  Â  Â  Â  Â  Â  Â (d) Infinite

20.) The position vector of the point which divides the jpin of points with position vectors and in the ratio 1:2 is

(a)Â

(b)

(d)

(d)

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