Question

The resultant to two Vectors A and B is R when vector A is reserved and again added to B the resultant turns through 90° .find the relation between A and B

Answer 1

Answer:

Explanation:

=> Suppose angle between them is θ and resultant of both angle R₁  make angle α with B

So, tan(α) = Asin(θ)/B + A cos (θ) ...(1)

=> direction of A get reversed

here, angle between B and reversed A vector is (180⁰ - θ).

=> Suppose new resultant R₂ make angle β with B.

tan(β) = A sin (180⁰-θ)/B + A cos (180⁰-θ) = Asin(θ)/B-Acos(θ) ...(2)

=> As per the question, α + β =90⁰

tan(α + β) = tan(90⁰)

tan(α) + tan(β) = tan (90⁰)

tan(α) + tan(β) / 1 - tan(α) * tan(β) = 1/0

tan(α) * tan(β) = 1

Placing the values from (1) and (2)

( Asin(θ) /B+Acos(θ)) ( Asin(θ)/ B-Acos(θ)) = 1

A^2 sin^2θ = B^2 - A^2 cos^2 θ

A^2 (sin^2θ + cos^2θ) = B^2

A^2 = B^2

A = B

Thus, the relation between the two vectors A and B is 'A=B'.