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Vector Addition

Let a⃗ and b⃗...

Question

Let $\to a$ and $\to b$ be two non -null vectors such that $| \to a + \to b | = | \to a - 2 \to b |$ . Then the value of $\frac{| \to a |}{| \to b |}$ may be

A

\frac{1}{4}

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B

\frac{1}{8}

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C

1

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D

2

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Solution

The correct options are
C 1
D 2
$| \to a + \to b | = | \to a - 2 \to b |$
Squaring on both sides,
$a^{2} + b^{2} + 2 a b cos θ = a^{2} + 4 b^{2} - 4 a b cos θ$
$cos θ = \frac{b}{2 a} \leq 1$
$∴ b \leq 2 a$
$\frac{a}{b} \geq \frac{1}{2}$
Hence, the possible answers are 1 and 2 according to options.

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