Question

Let for two vector A and B, sum (A + B) is perpendicular to the difference (A – B). Find the ratio A/B of their magnitudes
(1) 0 (2) 1 (3) 2 (4) 4

Answer 1

Answer:

(A+B).(A-B)=0

A^2-B^2=0

A^2=B^2

A=B

A/B=1

OPTION (2)

Answer 2

take the sum (A+B) and (A-B) as vector.......

now,

their,dot product=ABcos∅

since ∅=90

(A+B).(A-B)=ABcos90

A^2-AB+BA-B^2=0

A^2=B^2

so,

now here there are three,cases

A=-B (from here A/B=-1)

B=-A(from.hereA/B=-1)

A=B(from here A/B=1)

since we have focus on it's magnitude and magnitude can never be negative

so

from.third case,A/B=1✓✓✓✓✓