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Expert-verified Found in: Page 355 ### Physics For Scientists & Engineers

Book edition 9th Edition
Author(s) Raymond A. Serway, John W. Jewett
Pages 1624 pages
ISBN 9781133947271 # Use the definition of the vector product and the definitions of the unit vectors $\stackrel{\mathbf{\to }}{\mathbf{i}}{\mathbf{,}}\stackrel{\mathbf{⇀}}{\mathbf{j}}{\mathbf{,}}{\mathbit{a}}{\mathbit{n}}{\mathbit{d}}\stackrel{\mathbf{⇀}}{\mathbf{k}}$to prove Equations 11.7. You may assume the x axis points to the right, the y axis up, and the z axis horizontally toward you (not away from you). This choice is said to make the coordinate system a right-handed system.

$\stackrel{^}{i}×\stackrel{^}{j}=1\stackrel{^}{k}$

See the step by step solution

## Step 1: Define vector product

In physics and astronomy, the vector product and the scalar product are the two methods of multiplying vectors that are used the most. Taking the product of the magnitude of the vector times the sine of the angle between them yields the magnitude of the vector product of two vectors.

## Step 2: To find the vector product

By vector product of the two vectors are we get

$\stackrel{\to }{A}×\stackrel{\to }{B}=ABsin\theta$

The angle between the vectors is

To Prove that

$\stackrel{^}{i}×\stackrel{^}{i}=\stackrel{^}{j}×\stackrel{^}{j}=\stackrel{^}{k}×\stackrel{^}{k}=0....\left(1\right)$

$\stackrel{^}{i}×\stackrel{^}{j}=-\stackrel{^}{j}×\stackrel{^}{i}=\stackrel{^}{k}....\left(2\right)$

$\stackrel{^}{j}×\stackrel{^}{k}=-\stackrel{^}{k}×\stackrel{^}{j}=\stackrel{^}{i}.....\left(3\right)$

$\stackrel{^}{k}×\stackrel{^}{i}=-\stackrel{^}{i}×\stackrel{^}{k}=\stackrel{^}{j}.....\left(4\right)$

The two vectors $\stackrel{^}{i}$ are $\stackrel{^}{i}$ and are parallel, the angle between them be zero

From the first equation as$\stackrel{^}{i}×\stackrel{^}{i}=1.1sin{0}^{ο}$

$\stackrel{^}{i}×\stackrel{^}{j}=1×1sin{90}^{ο}$

$=1\stackrel{^}{k}$ ### Want to see more solutions like these? 