Question

Find the unit vector in the direction of the vector $\vec{a}=\hat i + \hat j+2\hat k$

Answer 1

Given Vector,

a = i + j + 2k

Now, Magnitude of the vector a = |a| = √(1)² + (1)² + (2)²

= √6

Now, Unit vector in the direction of this vector will be given by,

unit vector = (a vector)/magnitude of vector

∴ unit vector =  (i + j + 2k)/√6

Now, it will have magnitude equals to one only, but it is in vector form.

Hope it helps.