   Chapter 12.3, Problem 12E

Chapter
Section
Textbook Problem

# If u is a unit vector, find u · v and u · w. To determine

To find: A dot product uv and uw .

Explanation

Given:

u is a unit vector.

Formula:

Write the expression to find uv in terms of θ .

uv=|u||v|cosθ (1)

Here,

|u| is the magnitude of vector u,

|v| is the magnitude of vector v, and

θ is the angle between vectors u and v.

Consider the right angle triangle formed by u and v.

Write the expression to find magnitude of v (|v|) .

|v|=|u|cosθ (2)

As u, and w are the unit vectors, the value of |u| and |w| is 1.

From the diagram, the angle between u and v is 45° .

In equation (2), substitute 1 for |u| and 45° for θ .

|v|=(1)cos(45°)=(1)(0.707)=0

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### Find more solutions based on key concepts 