Question

A unit vector in the direction of the vector a = (2i - 3j + 6k) is

A. (i - 3/2 j + 3k)

B. (2/5 i - 3/5 j + 6/5 k)

C. (2/7 i - 3/7 j + 6/7 k)

D. none of these

Answer 1

Answer is : C. (2/7 i - 3/7 j + 6/7 k)

Tip – A vector in the direction of another vector ai + bj + ck is given by λ(ai + bj + ck) and the unit vector is given by 

So, a vector parallel to vector a = 2i - 3j + 6k is given by λ(2i - 3j + 6k) where λ is an arbitrary constant.

Now, \(|\overset{\rightarrow}{a}|\) = \(\sqrt{2^2+3^2+6^2}\) = 7

Hence, the required unit vector