Let a be the two dimensional vector <-2, 4> Consider a general vector b ne 0 whose position vector makes an angle theta with the x-axis. Explain why, no matter what b is, the tip of the position vector of b/(|b|) is on the unit circle.

Question

Let a be the two dimensional vector <-2, 4>
Consider a general vector

b \neq 0

whose position vector makes an angle

θ

withthe x-axis.
Explain why, no matter what b is, the tip of the positionvector of

\frac{b}{| b |}

is on the unit circle.

Answer 1

\frac{b}{| b |}

in terms of magnitude =1 { Any vector divided by its magnitude equals 1 (unit vector) }
the radius of a unit circle also = 1
therefore the tip of

\frac{b}{| b |}

must lie on the unit circle.

Answers (1)