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Chapter 1: Q25DQ (page 27)

If A鈫�.B鈫�=0 does it necessarily follow that A = 0 or B= 0? Explain. (b) If A鈫�脳B鈫�=0A鈫� = 0, does it necessarily follow that A = 0 or B = 0? Explain.

Short Answer

Expert verified

Given-

A鈫�.B鈫�=0

A鈫�脳B鈫�=0

Step by step solution

01

To Prove

Necessarily follow that ,A=0 or B=0

02

(Explanation , A→. B→=0then it is necessary A=0,B=0)If A→=0, B→=0

So, it doesn鈥檛 necessarily follow that A=0 or B=0 or it can be the case A鈫�perpendicularB鈫�.

03

(Explanation for A→×B→=0)

A鈫�脳B鈫�=ABsin胃

A鈫�脳B鈫�=0,ifA鈫�=0orB鈫�=0

Or A鈫�,B鈫�are in same direction or in opposite direction.

Hence it is not necessarily required for A and B =0 for A鈫�脳B鈫�=0

04

(Conclusion)

For

A鈫�.B鈫�=0

A鈫�脳B鈫�=0

It is doesn鈥檛 necessarily required A=0 or B=0.

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