First slide

Vectors

Question

The resultant of vectors A and B is R₁ . On reversing the direction of vector B, the resultant becomes R₂.
What is the value of $R_{1}^{2} + R_{2}^{2}$ ?

Easy

A

A² + B²
B

A² $-$ B²
C

2(A² + B²)
D

2 (A² $-$ B²)

Solution

We have, $R_{1}^{2} = A^{2} + B^{2} + 2 A B \cos θ$
and $R_{2}^{2} = A^{2} + B^{2} + 2 A B \cos θ$
$∴ R_{1}^{2} + R_{2}^{2} = 2 (A^{2} + B^{2})$

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