if vectorA+ vectorB = vecorA - vector B what is the relation between A and B
SDR:
Are the magnitudes of A+B and A-B equal
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here,
A^ + B^ = A^ - B^
take square both sides
(A^ + B^)² = ( A^ - B^)²
use formula,
|A + B | = √( |A|² + |B|² + 2|A||B|cos∅)
|A - B| = √(|A|² + |B|² -2|A | |B|cos∅)
use this in above ,
|A|² +| B|² +2|A | | B | cos∅ = |A|² + |B|² -2|A||B| cos∅
4|A| |B| cos∅ =0
cos∅ = 0
hence, ∅ = 90°
hebce, A and B are perpendicular to each other .
A^ + B^ = A^ - B^
take square both sides
(A^ + B^)² = ( A^ - B^)²
use formula,
|A + B | = √( |A|² + |B|² + 2|A||B|cos∅)
|A - B| = √(|A|² + |B|² -2|A | |B|cos∅)
use this in above ,
|A|² +| B|² +2|A | | B | cos∅ = |A|² + |B|² -2|A||B| cos∅
4|A| |B| cos∅ =0
cos∅ = 0
hence, ∅ = 90°
hebce, A and B are perpendicular to each other .
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