Question

"
Let A = (i + j) and, B = (2î –j ). The magnitude of a coplanar vector C such that A .C =B.C = A·B, is given
by
(JEE Main 2018)
(A)-√9/√12. (B)-√5/√9. (C)-√20/√9. (D)-√10/√9​

Answer 1

Answer:

ANSWER

Any vector in the plane b and c is

r=b+λc=(i+2j+k)+λ(i+j−2k)

=(1+λ)i+(2+λ)j+(−1−2λ)k

Projection of r on a is =

∣a∣

r.a

=

4+1+1

2(1+λ)−(2+λ)−(1+2λ)

=

6

−λ−1

∴

6

−λ−1

=±

3

2

⇒−λ−1=±2⇒λ=−3,1

Hence r=−2i−j+5k and r=2i+3j−3k