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STATEMENT-1 : The vector hati bisects th...

STATEMENT-1 : The vector `hati` bisects the angle between the vectors `hati-2hatj-2hatk` and `hati+2hatj+2hatk`.
And
STATEMENT-2 : The vector along the angle bisector of the vector `veca` and `vecb` is given by `+-((veca)/(|veca|)+-(vecb)/(|vecb|))` where `|veca|.|vecb|ne 0`
Let `vecu` and `vecv` be unit vectors inclined at an angle `theta` such that for some vector `vecw,vecw+vecwxxvecu=vecv`

A

Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-3

B

Statement-1 is True, Statement-2 is True, Statement-2 is not a correct explanation for Statement-3

C

Statement-1 is True, Statement-2 is False

D

Statement-1 is False, Statement-2 is True

Text Solution

Verified by Experts

The correct Answer is:
3
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If the sides of an angle are given by vectors veca=hati-2hatj+2hatk and vecb=2hati+hatj+2hatk , then find the internal bisector of the angle.

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Assertion: The angle between the two vectors (hati+hatj) and (hatj_hatk) is (pi)/(3) radian. Reason: Angle between two vectors vecA and vecB is given by theta=cos^(-1)((vecA.vecB)/(AB))

Assertion : The angle between the two vectors (hati + hatj) and (hatj + hatk) is (pi)/(3) radian. Reason : Angle between two vectors vecA and vecB is given by theta = cos^(-1)((vecA*vecB)/( AB))