Question

what is the unit vector perpendicular to the vector 4j-3k

Answer 1

Let the given vector be, a = 0i+4j-3k
and, let another vector (unit vector) be, b = xi+yj+zk

Now, their dot-product must be zero.
b.a = 0 .................................by the perpendicularity condition.
(xi+yj+zk).(0i+4j-3k) = 0
4y-3z = 0 ......................(equation)

Now, take |b^{^}| = 1 ...................as, b is a unit vector.

Therefore, taking the arbitrary values, y = 3 and z = 4 for satisfying the above (equation), we get,

b = 3j+4k

Then, the required unit vector, b^{^} = b / |b^{^}|
= (3j+4k) / 1
= 3j+4k .