The vectors A and B are such that |A + B| = |A – B|, then the angle between the two vectors is:
ETEA 2013
Physics
Scalars and Vectors
Basic Concepts of Vectors
Elimination Tool:
Think of A and B as having a ∅ angle.
The vector A + B’s resultant is as follows:
√(A²+B²+2AB cos∅) = R
The A-B vector’s resultant is provided as
(A²+B²-2AB cos∅) = R
As stated in the question,
|A+B| = |A-B|
√A² + B² + 2AB cos∅ = √(A² + B²-2AB cos∅)
Resolving,
4ABcos∅ = 0
Cos ∅ = 0.
∅ = 90°
Think of A and B as having a ∅ angle.
The vector A + B’s resultant is as follows:
√(A²+B²+2AB cos∅) = R
The A-B vector’s resultant is provided as
(A²+B²-2AB cos∅) = R
As stated in the question,
|A+B| = |A-B|
√A² + B² + 2AB cos∅ = √(A² + B²-2AB cos∅)
Resolving,
4ABcos∅ = 0
Cos ∅ = 0.
∅ = 90°