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Question

Assertion :If ^u and ^v are unit vectors inclined at an angle α and ^a is a unit vector bisecting the angle between them, then ^a=^u+^v2cos(α/2) Reason: If ABC is an isosceles triangle with AB=AC=1, then the vector representing bisector of angle A is AB+AC2

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
Both Assertion and Reason are incorrect
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Solution

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
In an isosceles triangle ABC in which AB=AC, the median and bisector from A must be same line so statement 2 is true
AD=u+v2
|AD|2=.14[|u|2+|v|2+2uv]
=14[2+2cosα]
=cos2α/2
Unit vector along AD=12cos(α/2)(u+v)

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