Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
BITSAT2013MathematicsVector AlgebraActual

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

Options

  1. A2
  2. B-2
  3. C-1
  4. D-4

Correct answer

D. -4

Step-by-step solution

If given vectors are coplanar, then there exists two scalar quantities x and y such that 2 i - j + k =x( i +2 j -3 k )+y(3 i +a j +5 k ) Comparing coefficient of i , j and k on both sides of (1) we get x+3 y=2,2 x+a y=-1,-3 x+5 y=1 (2) Solving first and third equations, we get x =1 / 2, y =1 / 2 Since the vectors are coplanar, therefore these values of x and y will satisfy the equation 2 x+a y=-1 2(1 / 2)+a(1 / 2)=-1 a=-4

Practice Vector Algebra on Quantrex Academy →

More from Vector Algebra

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 2024Let 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 2024If 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 2024A 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 2023If a = i + j + k , a b =1 and a b = j - k , then b is 2023107. 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 2022If 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 2021If 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 2020 Full Vector Algebra list All BITSAT PYQs