The sum and difference of two vector are equal in magnitude. Prove that two vectors are perpendicular
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Answered by
192
Hi.
Let the two vectors be A and B (I'm writing w/o the arrow heads)
Then according to question
|A+B| = |A-B|
squaring both sides
|A+B|² = |A-B|²
A² + B² + 2A.B = A²+ B² -2A.B
(where A.B is the dot product of A and B)
Cancelling A² + B² from both sides we get
4A.B = 0
A.B=0 (4 can't be zero)
ABcosX = 0
(X is angle between A and B)
CosX = 0
X = 90
ie A & B are perpendicular to each other.
Let the two vectors be A and B (I'm writing w/o the arrow heads)
Then according to question
|A+B| = |A-B|
squaring both sides
|A+B|² = |A-B|²
A² + B² + 2A.B = A²+ B² -2A.B
(where A.B is the dot product of A and B)
Cancelling A² + B² from both sides we get
4A.B = 0
A.B=0 (4 can't be zero)
ABcosX = 0
(X is angle between A and B)
CosX = 0
X = 90
ie A & B are perpendicular to each other.
Answered by
11
Answer:
answer of this question is 90 degree...
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