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Statement 1: If vec ua n d vec v are un...

Statement 1: If ` vec ua n d vec v` are unit vectors inclined at an angle `alphaa n d vec x` is a unit vector bisecting the angle between them, then ` vec x=( vec u+ vec v)//(2sin(alpha//2)dot` Statement 2: If `"Delta"A B C` is an isosceles triangle with `A B=A C=1,` then the vector representing the bisector of angel `A` is given by ` vec A D=( vec A B+ vec A C)//2.`

A

Both the statements are true, and Statement 2 is the correct explanation for Statement 1.

B

Both the statements are true, but Statement 2 is not the correct explanation for Statement 1.

C

Statement 1 is true and Statement 2 is false.

D

Statement 1 is false and Statement 2 is true.

Text Solution

Verified by Experts

The correct Answer is:
D
We know that the unit vector along bisector of unit vectors `vecu and vecv` is `(vecu + vecv)/(2cos(theta//2))`, where `theta` is the angle between vectors `vecu and vecv`.
Hence, Statement 1 is false, however, Statement 2 is true.
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