Chapter 9: Q. 7 (page 612)

In Problems 7–16,
(a) find the dot product $v \cdot w$ ;
(b) find the angle between v and w;
(c) state whether the vectors are parallel, orthogonal, or neither.
$v = i - j w = i + j$

Short Answer

Expert verified

Part a. $v \cdot w = 0$

Part b. The angle between the vectors is $90 °$

Part c. The vectors are orthogonal

Step by step solution

Part (a) Step 1. Given Information

We are given two vectors $v = i - j$ and $w = i + j$ .

We need to find their dot product, the angle between the two vectors, and the nature of the two vectors.

Part (a) Step 2. Find the dot product

The dot product for the given vectors is given as

$v \cdot w = (i - j) \cdot (i + j) v \cdot w = 1 \cdot 1 + (- 1) \cdot 1 v \cdot w = 1 - 1 v \cdot w = 0$

Part (b) Step 1. Find the angle

The angle between the vectors vand wis

$\cos θ = \frac{v \cdot w}{|v| |w|}$

Now as $v \cdot w = 0$ so we get

$\begin{array}{rcl} \cos θ & = & \frac{0}{|v| |w|} \\ \cos θ & = & 0 \\ θ & = & 90 ° \end{array}$

Part (c) Step 1. Identify the nature of the vectors

As the angle between the two vectors is $90 °$ , so the given two vectors v and w are othrogonal.

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In Problems 7–16,
(a) find the dot product $v \cdot w$ ;
(b) find the angle between v and w;
(c) state whether the vectors are parallel, orthogonal, or neither.
$v = i - j w = i + j$

Short Answer

Step by step solution

Part (a) Step 1. Given Information

Part (a) Step 2. Find the dot product

Part (b) Step 1. Find the angle

Part (c) Step 1. Identify the nature of the vectors

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In Problems 7–16,(a) find the dot product v·w; (b) find the angle between v and w;(c) state whether the vectors are parallel, orthogonal, or neither.v=i-jw=i+j

Short Answer

Step by step solution

Part (a) Step 1. Given Information

Part (a) Step 2. Find the dot product

Part (b) Step 1. Find the angle

Part (c) Step 1. Identify the nature of the vectors

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Discrete Mathematics

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Calculus

Mechanics Maths

Probability and Statistics

Study anywhere. Anytime. Across all devices.

In Problems 7–16,
(a) find the dot product $v \cdot w$ ;
(b) find the angle between v and w;
(c) state whether the vectors are parallel, orthogonal, or neither.
$v = i - j w = i + j$