Question

vector A and B are mutually perpendicular. Prove that Component of A+ B in the direction of a minus B will be A2-B2/root A2+B2

Answer 1

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◆ Answer -

R = A^2-B^2 / √(A^2+B^2)

● Explanation -

Magnitude of A-B is given as -

|A-B| = √(A^2 + B^2 - 2AB.cos90)

|A-B| = √(A^2 + B^2 - 2AB × 0)

|A-B| = √(A^2 + B^2)

Unit vector along A-B will be given as -

Unit vector = (A-B) / |A-B|

Unit vector = (A-B) / √(A^2+B^2)

Component of A+B in direction of A-B will be -

R = (A+B).(A-B) / √(A^2+B^2)

R = A^2-B^2 / √(A^2+B^2)

Therefore, component of A+B in direction of A-B will be A^2-B^2 / √(A^2+B^2) .

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