CAREER POINT

PRACTICEWORKJEE (Main)SUB : MATH

VECTORS

1.If are vectors such that then [AIEEE-2002](a) 16 (b) 64 (c) 4 (d) 8 2. If are vectors such that and then angle between vector and is [AIEEE-2002] (a)

(b)

(c) (d)

3. If then what will be the

value of given that [AIEEE-2002]

(a) 25 (b) 50 (c) -25 (d)-50 4.

and are two vectors and is a vector such that then [AIEEE-2002]

(a)

(b)

(c)

(d)

5.If then

[AIEEE-2002]

(a) abc (b) -1 (c) 0 (d) 2 6.If the vectors are such that form a right handed system, then is [AIEEE-2002]

(a) (b) (c) (d)

7.If and the angle between is then is equal to

[AIEEE-2002]

(a)16(b)32

(c)48

(d)64

8.Let If is a unit vector such that and then is equal to [AIEEE-2003]

(a) 0 (b) 1 (c) 2 (d) 3

9.The vectors and are the sides of a triangle ABC. The length of the median through A is

[AIEEE-2003]

(a)

(b) (c) (d)

10.Consider points A,B,C and D with position vectors respectively. Then, A, B, C, D is a [AIEEE-2003]

(a) square

(b) rhombus

(c) rectangle

(d) None of these11.If are three non-coplanar vectors, then equals

[AIEEE-2003]

(a) 0

(b)

(c)

(d)

12.

are three vectors, such that

then is equal to [AIEEE-2003]

(a) 0 (b) 7 (c) 7 (d) 1 13.Let be non-zero vectors such that If ( is the acute angle between the vectors , then sin ( equals [AIEEE-2004]

(a) (b) (c) (d) 14.Let be such that . If the projection is equal to that of are perpendicular to each other, then are equals

[AIEEE-2004]

(a) 2 (b) (c) (d) 1415.Let be three non-zero vectors such that no two of these are collinear. If the vector is collinear with is collinear with (( being some non-zero scalar), then equals [AIEEE-2004]

(a) (b) (c) (d)

16.Let a, b and c be distinct non-negative numbers. If the vectors and lie in a plane, then c is

[AIEEE-2005]

(a) the harmonic mean of a and b

(b) equal to zero

(c) the arithmetic mean of a and b

(d) the geometric mean of a and b17.If C is the mid point of AB and P is any point

outside AB, then [AIEEE-2005]

(a)

(b)

(c)

(d)

18.The value of a, for which the points, A, B, C with position vectors and , respectively are the vertices of a right angled triangle with are

[AIEEE-2006]

(a) 2 and 1

(b) 2 and 1

(c) 2 and 1

(d) 2 and 1 19.If where are any three vectors such that

[AIEEE-2006](a) inclined at angle of between them (b) perpendicular (c) parallel

(d) inclined at angle of between them 20.Let and

If the vector lies in

the plane of , then x equals

[AIEEE-2007]

(a) 0 (b) 1 (c) 4 (d) 2 21.The non-zero vectors are related by . Then, the angle between is [AIEEE-2008]

(a) ( (b) 0 (c) (/4 (d) (/2

22.The vector lies in the plane of the vectors and bisects the angle between . Then, which one of the following gives possible values of ? [AIEEE-2008]

(a)

(b)

(c)

(d)

23. If the vectors , and are mutually orthogonal, then = [AIEEE-2010]

(a)(2,3) (b)(2,3) (c)(3,2) (d)(3,2)24.If , then the value of is

[AIEEE-2011]

(a)-3 (b)5 (c)3 (d)-5

25.Let be two unit vectors. If the vectors are perpendicular to each other,then the angle between is [AIEEE-2012] (a) (b)

(c)

(d)

26.If the vectors and are the sides of a triangle ABC, then the length of the median through A is

[JEE MAINS-2013]

(a) (b) (c) (d)

27.If , then is equal to

[JEE MAINS-2014]

(a) 2 (b) 3 (c) 0 (d) 1

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