Find the unit vector perpendicular to each of the vectors: 3i+j+2k AND 2i-2j+4k

CBSE Class 11
1

Find the unit vector perpendicular to each of the vectors: 3i+j+2k AND 2i-2j+4k.

2

A vector perpendicular to both of the given vectors can be found out by finding the cross product of the two vectors.
A = (3i+j+2k) x (2i-2j+4k.) = 8i -8j -8k
unit vector = A / |A| = (8i -8j -8k) / √(82+82+82) = (i-j-k)/√3.