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Standard XII

Mathematics

Cosine Rule

Two vectors a...

Question

Two vectors $¯ a and ¯ b$ are at an angle of 60⁰ with each other. Their resultant makes an angle of 45⁰ with $¯ a$ . If $| ¯ b |$ =2 units, then $| ¯ a |$ is

$\sqrt{3}$

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$\sqrt{3} - 1$

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$\sqrt{3} + 1$

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$\sqrt{3} / 2$

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Solution

The correct option is B
$\sqrt{3} - 1$

$t a n 45^{0} = \frac{2 s i n 60^{0}}{a + 2 c o s 60^{0}} = \frac{\sqrt{3}}{a + 1} o r 1 = \frac{\sqrt{3}}{a + 1} o r a + 1 = \sqrt{3} o r a = \sqrt{3} - 1$

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The correct option is B
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$t a n 45^{0} = \frac{2 s i n 60^{0}}{a + 2 c o s 60^{0}} = \frac{\sqrt{3}}{a + 1} o r 1 = \frac{\sqrt{3}}{a + 1} o r a + 1 = \sqrt{3} o r a = \sqrt{3} - 1$