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Vector Addition

Assertion :If...

Question

Assertion :If $\to u$ and $\to v$ are unit vectors inclined at an angle $α$ and $\to x$ is a unit vector bisecting the angle between them, then $\to x = \frac{\to u + \to v}{2 sin (α / 2)}$ Reason: If $Δ A B C$ is an isosceles triangle with $A B = A C = 1,$ then the vector representing the bisector of $∠ A$ is given by $\to A D = \frac{\to A B + \to A C}{2}$ .

A

Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

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B

Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

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C

Assertion is correct but Reason is incorrect

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D

Assertion is incorrect but Reason is correct

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Solution

The correct option is D Assertion is incorrect but Reason is correct
according to the theoram of isosceles theoram angle bisector is
$\to A D = \frac{\to A B + \to A C}{2}$
So reason is correct to find angle bisector
But the given bisector id wrong acc. to calculation formula

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