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Chapter 9: Q. 14 (page 228)

Evaluate the dot product of the three pairs of vectors in Figure

Short Answer

Expert verified

A→·B→=11.5C→·D→=-4.6E→·F→=0

Step by step solution

01

Step 1. Given Information

We have

The dot product is the sum of the product of the component where this dot product is called the scalar product.

For two vector A and B and there is an angle x between then the dot product these two vectors is given by

A→·B→=ABcosαC→·D→=CDcosαE→·F→=EFcosα

02

Step 2. Part a). A and B are the magnitudes and α is the angle

We are given vectors by A=3and B=5and the angle is role="math" localid="1648018330260" α=40°

So,

A→·B→=ABcosα=(3)(5)cos40°=11.5

03

Step 3. Part b). C and D are the magnitudes and α is the angle 

The magnitude of the vector C=2and D=3and the angle is α=140°

So,

C→·D→=CDcosα=(2)(3)cos140°=-4.6

04

Step 4. Part c). E and F are the magnitudes and α is the angle

The magnitude of the vector E=3and F=4and the angle is α=90°

E→·F→=EFcosα=(3)(4)cos90°=0

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