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Chapter 1: Q26E (page 27)

IfA鈫�= 0 for a vector in the xy-plane, does it follow that Ax = -Ay? What can you say about Ax and Ay?

Short Answer

Expert verified

Given- A鈬赌and B鈬赌are vector The sum of number of vectors that for the sum of two vectors is geometrically represented by the diagonal of parallelogram whose side represent the two vectors being added.

A鈬赌=0,for a vector in the xy plane.

Step by step solution

01

To Prove

Ax=-Ay

02

(Explainationand proof  of Ax = -Ay) =0

If A鈬赌=0

Such that A鈬赌is in xy plane.

i.e.A鈬赌= Ax喂^+Ay鈬赌J^

03

(Explaination )

Magnitude of A鈬赌=Ax+localid="1663675123183" AY2

A鈬赌= 0 localid="1663675191128" =Ax2+Ay2

localid="1663677147446" Ax2+localid="1663677163472" AY2=0

The only case possible is

Ax= Ay=0

04

(Conclusion)

It is proved

Axis not equal to -Ay

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