If a unit vector makes angles and an acute angle θ with then find θ and hence, the components of .

Question

Philoid · Accepted Answer

Let

Given that it is a unit vector,

So, ……(1)

Let be the angle with respectively.

Then,

(given)

Putting value of x,y, z in equation (1)

(Squaring both sides)

As should be acute,

Components of are the coefficients of , which are,