Question

How do I find the magnitude of the vector `v=21(cos18°i+sin18°j)?`?

Answer 1

Given, `vec v =21(cos 18 i + sin 18 j)`

Angle between `21 cos 18 i` and `21 sin 18 j` is `90`

So, `|vec v| = sqrt((21 cos 18)^2 + (21 sin 18)^2) = sqrt(21^2(cos ^2 18 + sin ^2 18))=sqrt(21^2×1)=21`

Answer 2

`|| bbv ||=21`

Explanation:

If `bbv =v_1 bbi +v_2 bbj`, then the magnitude of `bbv` is `|| bbv ||=sqrt(v_1^2+v_2^2)`

`bbv =21cos18 bbi +21sin18 bbj`.

So

`|| bbv ||=sqrt((21cos18)^2+(21sin18)^2)=sqrt(441cos^2 18+441sin^2 18)=sqrt(441(cos^2 18+sin^18))=sqrt441=21`