If the magnitude of sum of two vectors

Asked by admin @ 26/08/2021 in Physics viewed by 316 People

If the magnitude of sum of two vectors is equal to the magnitude of difference of the two vectors the angle between these vector is

a) 90 b) 45 c) 180 d)0

Answered by admin @ 26/08/2021

Here is the solution :

let the two vectors be a and b,

According to the question,

|a-b| = |a+b|,

from parallelogram law of vectors, we know that,

|p±q| = √(p² + q² ± 2pq cos ∆)

where, ∆ = angle between the vectors p and q,

=> √(a²+b²+2abcos∆) = √(a²+b²-2abcos∆)

squaring on both sides and cancelling a and b both sides,

=> 2abcos∆ = -2abcos∆

=> 4abcos∆ = 0,

|a| ≠ |b| ≠ 0,

=> cos∆ = 0,

=> ∆ = odd integral multiples of 90°,

=> ∆ = 90°, 270°...

since 270° isn't in the options given, (a) 90° will be the correct answer.

therefore , the angle between the 2 vectors is 90°.

Hope you understand, Thanking you,

Bunti 360!

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