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Chapter 1: Q24DQ (page 27)

Show that, no matter what A鈫�and B鈫�are, A鈫�.A鈫�脳B鈫� =0

Short Answer

Expert verified

Given-

A鈫�and B鈫�vectors.

Step by step solution

01

Step1- To Prove

A鈫�.A鈫�脳B鈫�=0

Magnitude is equal to zero

02

Step 2 Explaination (A→×B→) =0

We know that A鈫�脳B鈫�is vector Perpendicular to both A鈫�and B鈫�Let鈥檚 say that A鈫�and B鈫�in xy plane. Then A鈫�and B鈫�will be along z-axis.

Hence, A鈫�脳B鈫�=0

03

Step3 (Explaination for A→.A→×B→=0) 

Since, A鈫�which lies in xy plane and A鈫�and B鈫� lies along zaxis are perpendicular to each other.

A鈫�.A鈫�脳B鈫�=0

04

Step 4- (Conclusion)

It is proved

A鈫�.A鈫�脳B鈫�=0

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Most popular questions from this chapter

In each case, find the x- and y-components of vectorA鈫�: (a)A鈫�=5.0i^-6.3j^; (b)A鈫�=11.2j^-9.91i^; (c)A鈫�=-15.0i^+22.4j^; (d)A鈫�=5.0B鈫�, whereB鈫�=4i^-6j^.

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