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

Question

Philoid · Accepted Answer

Let unit vector r⃗ have (r₁, r₂, r₃) components.

⇒ r⃗ = r₁î + r₂ j + r₃ k̂

Since, r⃗ is a unit vector.

⇒ |r⃗ | = 1

Also, given that r⃗ makes angles with î,with ĵ and an acute angle θ with k̂

Then, we have:

(∵ |r⃗ | = 1)

Also,

⇒ cosθ = r₃ (∵ |r⃗ | = 1)

Now, |r⃗ | = 1

⇒ √ (r₁² + r₂² + r₃²) = 1

∴

∴ and the components of r⃗ are -