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Chapter 9: Q. 15 (page 228)

Evaluate the dot product of the three pairs of vectors in

Figure

Short Answer

Expert verified

a).A鈫�路B鈫�=-2.7

b).role="math" localid="1648057299716" C鈫�路D鈫�=-20

c).E鈫�路F鈫�=10

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 Aand Band there is an angle 伪between then the dot product these two vectors is given by

A鈫�路B鈫�=ABcos伪C鈫�路D鈫�=CDcos伪E鈫�路F鈫�=EFcos伪

02

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

We are given by A=3and B=5and the angle is伪=110掳

So,

A鈫�路B鈫�=ABcos伪=(2)(4)cos110掳=-2.7

03

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

The magnitude of the vector by C=4and D=5and the angle is role="math" localid="1648059175573" 伪=180掳

So,

C鈫�路D鈫�=CDcos伪=(4)(5)cos180掳=-30

04

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

The magnitude of the vector by E=4and F=3and the angle is 伪=30掳

So,

E鈫�路F鈫�=EFcos伪=(4)(3)cos30掳=10

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