Question

Let `veca -2hati + hatj +hatk , vecb =hati + 2hatj +hatk and vecc = 2hati -3hatj +4hatk . A " vector " vecr " satisfying " vecr xx vecb = vecc xx vecb and vecr . Veca =0` is
A. ` -2hati =2hatj +2hatk`
B. ` -2hati +hatj +3hatk`
C. ` 3hati+2hatj +4hatk`
D. ` hati - 5hatj +3hatk`

Answer 1

Correct Answer - D
we have,
` vecr xx vecb = vecc xx vecb`
` Rightarrow (vecr -vecc) xx vecb = vec0 Rightarrow vecr -vecc= lambda vecb Rightarrow vecr = vecc + lambda vecb`
Now, `vecr.veca =0 Rightarrow (vecc + lambda vecb) .veca =0 Rightarrow lambda = ( vecc .veca)/( vecb .veca) = -1`
Hence, ` vecr = vecc -vecb=hati - 5hatj + 3hatk`