# Determine whether the following statements are true and give an explanation or counterexample. a. proj v u

## Question:

Determine whether the following statements are true and give an explanation or counterexample.

a. proj_{v}u = proj_{u}v.

b. If nonzero vectors u and v have the same magnitude, they make equal angles with u + v.

c. (u • i)^{2} + (u • j)^{2} + (u • k)^{2} = |u|^{2}.

d. If u is orthogonal to v and v is orthogonal to w, then u is orthogonal to w.

e. The vectors orthogonal to (1, 1, 1) lie on the same line.

f. If proj_{v}u = 0, then vectors u and v (both nonzero) are orthogonal.

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## Step by Step Answer:

**Related Book For**

## Calculus Early Transcendentals

**ISBN:** 978-0321947345

2nd edition

**Authors:** William L. Briggs, Lyle Cochran, Bernard Gillett