First slide

Scalars and Vectors

Question

If for two vector $\vec{A} and \vec{B}, sum (\vec{A} + \vec{B})$ is perpendicular to the difference $(\vec{A} - \vec{B})$ . The ratio of their magnitude is

Moderate

A

1
B

2
C

3
D

None of these

Solution

$(\vec{A} + \vec{B}) is perpendicular to (\vec{A} - \vec{B}) . Thus$
$\begin{array}{l} (\vec{A} + \vec{B}) \cdot (\vec{A} - \vec{B}) = 0 \\ or A^{2} + \vec{B} \cdot \vec{A} - \vec{A} \cdot \vec{B} - B^{2} = 0 \end{array}$
Because of commutative property of dot product $\vec{A} \cdot \vec{B} = \vec{B} \cdot \vec{A}$
$∴ A^{2} - B^{2} = 0 or A = B$
Thus the ratio of magnitudes A/B=1

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