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Vector Algebra — BITSAT Mathematics PYQs

25 previous year questions from Vector Algebra with answers and solutions. Numbered list, year tags, and one-tap solutions — built for serious JEE / NEET practice.

Vector Algebra — BITSAT Mathematics PYQs

Let a = i - k , b =x i + j +(1-x) k and c =y i +x j +(1+x-y) k . Then, [ a b ~ c ] depends on

Let ABC be a triangle and be a , b , c the position vectors of A , B , C respectively. Let D divide B C in the ratio 3: 1 internally and E divide AD in the ratio 4: 1 internally. L

If a =2 i + j +2 k , then the value of | i ( a i )|^2+| j ( a j )|^2+| k ( a k )|^2 is equal to

A vector perpendicular to the plane containing the vectors i -2 j - k and 3 i -2 j - k is inclined to the vector i + j + k at an angle

If a = i + j + k , a b =1 and a b = j - k , then b is

107. u and v are two non-collinear unit vectors such that | u + v 2 + u v |=1 . Then the value of | u v | is equal to

If a is a vector of magnitude 50 , collinear with the vector b =6 i -8 j - 15 2 k and makes an acute angle with the positive direction of Z - axis, then a is equal to

If r and s arenon-zero constant vectors and the scalar b is chosen such that | r +b s | is minimum, then the value of |b s |²+| r +b s |² is equal to

If a &#8594; , b &#8594; , c &#8594; are non-coplaner vectors such that b &#8594; &#215; c &#8594; = a &#8594; ; c &#8594; &#215; a &#8594; = b &#8594; ; a &#8594; &#215; b &#8594;

If a &#8594; = i ^ + 2 j ^ + 3 k ^ , b &#8594; = - i ^ + 2 j ^ + k ^ , c &#8594; = 3 i ^ + j ^ and a &#8594; + p b &#8594; is normal to c &#8594; , then p is equal to

In a &#8710; A B C , D , E , F are the mid-points of the sides B C , C A and A B respectively, the vector A D &#8594; is equal to

If h is the altitude of a parallelopiped determined by the vectors a ^ , b ^ , c ^ and the base is taken to be the parallelogram determined by a ^ and b ^ where a ^ = i ^ + j ^ + k

Let a ^ and b ^ are two non-collinear unit vectors. If u &#8594; = a ^ - a ^ &#183; b ^ b ^ and v &#8594; = a ^ &#215; b ^ , then | v &#8594; | is equal to

Let a, b and c be three vectors satisfying a b=(a c),|a|=|c|=1,|b|=4 and |b c|= 15 . If b-2 c = a , then equals

If the middle points of sides BC , CA & AB of triangle ABC are respectively D , E , F then position vector of centre of triangle DEF , when position vector of A, B, C are respectiv

The angle between any two diagonal of a cube is

If a , b , c are three unit vectors such that a + b + c = 0 , where 0 is null vector, then a b + b c + c a is :

If vectors 2 i - j + k , i +2 j -3 k and 3 i + aj +5 k are coplanar, then the value of a is

The unit vector perpendicular to the vectors 6 i +2 j +3 k and 3 i -6 j -2 k is -

If a .b =a .c and a b=a c , then correct statement is

Two vectors ( A ) and ( B ) are such that (| A + B |=| A - B | ). The angle between the two vectors will be-

The solution of differential equation (2 x d y d x -y=3 ) represents a family of

If (( a b )^2+( a b )^2=676 ) and (| b |=2 ) then (| a | ) is equal to

Which one of the following is the unit vector perpendicular to both ( a =- i + j + k ) and ( b = i - j + k ) ?

With respect to a rectangular cartesian coordinate system, three vectors are expressed as : ( a =4 i - j , b =-3 i +2 j ) and ( c =- k ) where ( i , j , k ) are unit vectors, along

If a → , b → , c → are non-coplaner vectors such that b → × c → = a → ; c → × a → = b → ; a → × b →

If a → = i ^ + 2 j ^ + 3 k ^ , b → = - i ^ + 2 j ^ + k ^ , c → = 3 i ^ + j ^ and a → + p b → is normal to c → , then p is equal to

In a ∆ A B C , D , E , F are the mid-points of the sides B C , C A and A B respectively, the vector A D → is equal to

Let a ^ and b ^ are two non-collinear unit vectors. If u → = a ^ - a ^ · b ^ b ^ and v → = a ^ × b ^ , then | v → | is equal to