Question

The vector parallel to the line of intersection of the planes `vecr.(3hati-hatj+hatk) = 1` and `vecr.(hati+4hatj-2hatk)=2` is :
A. `2hati+7hatj+13hatk`
B. `-2hati-7hatj+13hatk`
C. `2hati+7hatj+13hatk`
D. `-2hati+7hatj+13hatk`

Answer 1

Correct Answer - D
We know that the line of intersection of the planes `vecr.vecn_(1)=d_(1)` and `vecr.n_(2)=d_(2)` is parallel to `vecn_(1)xxvecn_(2)`.
Hence `vecn_(1)-3hati-hatj+hatk` and `vecn_(2)+4hatj-2hatk`
`:.` Required vector `=vecn_(1)xxvecn_(2)=|(hati,hatj,hatk),(3,-1,1),(1,4,-2)|=-2hati+7hatj+13hatk`