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# Consider the vector products and Give an example that ISBN: 9780321675460 31

## Solution for problem 23DQ Chapter 1

University Physics | 13th Edition

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Problem 23DQ

Consider the vector products and Give an example that illustrates the general rule that these two vector products do not have the same magnitude or direction. Can you choose vectors such that these two vector products are equal? If so, give an example.

Step-by-Step Solution:

Solution 23DQ Part A: Step 1: Any three random vector we will take say A,B and C . Among these let’s take B and C lie on one plane and the vector Alie on a plane perpendicular to the plane where B and C reside. The diagram is as follows, The vector A points into the page, perpendicular to the plane where B and C vector lie. Step 2: First let’s find A × (B × C). (B × C) gives a new vector Dsay, in the direction which is along the vector A by the right hand screw rule of vector cross product. As, vector A and vector D are in same direction, the angle between them will be 0 . So, , which is a null vector. Step 3: Now let’s calculate (A × B) × C . Here A × B will give a new vector E say. This vector will lie on the same plane where vector B and vector C lie. The magnitude will be, 0 E = A × B = A| || | 90 = A B ×| || | B . | || | Because the angle between vector A and vector B is 90 and sin 90 =1 we know. Now (A × B) × C = E × C = E C | || |= A B C | || || | Where is the angle between vector E and vector C. It can be clearly seen that, (A × B) × C / 0 . So, we proved that A × (B × C) = / (A × B) × C . Part B: Step 1: The above equation is true for any randomly chosen vectors. But for a very special case the magnitude and direction are same for both the sides. Let’s show it. Let’s take 3 mutually perpendicular vectors A,B and C along the 3 axes of a cartesian coordinate system respectively. 0 0 So, A × (B × C) = A × ( | || |n 90 ) = A × ( B| || |as sin 90 = 1. 0 A × (B × C) = A | || || | = 0. This is because, the vector formed by B × C is along the vector A and the angle between 0 them will be zero. And we know that sin 0 = 0. So, A × (B × C) = 0

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##### ISBN: 9780321675460

This textbook survival guide was created for the textbook: University Physics, edition: 13. This full solution covers the following key subjects: Vector, products, these, Example, give. This expansive textbook survival guide covers 26 chapters, and 2929 solutions. The answer to “Consider the vector products and Give an example that illustrates the general rule that these two vector products do not have the same magnitude or direction. Can you choose vectors such that these two vector products are equal? If so, give an example.” is broken down into a number of easy to follow steps, and 43 words. Since the solution to 23DQ from 1 chapter was answered, more than 252 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 23DQ from chapter: 1 was answered by , our top Physics solution expert on 05/06/17, 06:07PM. University Physics was written by and is associated to the ISBN: 9780321675460.

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