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

Answer :-

R = A² - B²/ √(A² + B²)

Explanation :-

Magnitude of A-B is given as -

| A - B | = √(A² + B² - 2AB.cos90)

= √(A² + B² - 2AB × 0)

= √(A² + B²)

Unit vector along A - B will be given as -

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

= (A - B) / √(A² + B²)

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

R = (A + B).(A - B) / √(A² + B²)

= A² + B² / √(A² + B²)

Therefore, Component of A + B in Direction of A - B will be A² - B² / √(A² + B²).

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