Question

If vectors A and B are such that A + B] = A= B,
then [A - B] may be equated to

(1)√3\2 [A]
(2) [A]

(3) √2A
(4) √3A​

Answer 1

Answer:

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Explanation:

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Answer 2

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√3\2[A]

The larger diagonal is representing the sum of vectors a and b.

The smaller diagonal is representing the difference of vectors a and b.

Using cos Rule in trigonometry,

We have |a+b|=sqrt(a*a +b*b+2*a*b*cos C)

where a and b are the two vectors and C is the angle between the two vectors a and b

and |a - b| =sqrt(a*a +b*b-2*a*b*cos C)

When |a+b|=|a - b|

Squaring both sides

(|a+b|)(|a+b|)=(|a-b|)(|a-b|)

We are left with

a*a+b*b+2*a*b*cosC =a*a+b+b-2*a*b*cosC

Cancelling and rearranging, we obtain

4*a*b*cosC = 0

cosC=0

We know that cos90 = 0

C = 90