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Vector Component

The ratio of ...

Question

The ratio of maximum and minimum magnitudes of the resultant of two vectors $¯ A$ and $¯ B$ is 3:2. The relation between A and B is:

A

A = 5 B

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B

5 A = B

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C

A = 3 B

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D

A = 4 B

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Solution

The correct option is B $A = 5 B$
$(\to A + \to B)_{m a x} = A + B$ .
$(\to A + \to B)_{m i n} = A - B$
Therefore, $\frac{A + B}{A - B} = \frac{3}{2}$
$\Rightarrow 2 A + 2 B = 3 A - 3 B$
$\Rightarrow A = 5 B$

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