AP EAMCET20228 Jul 2022Evening ShiftMathematicsVector AlgebraActual
If a and b are two non-collinear vectors and the vector a + b bisects the angle between a and b , then
Options
- A| a |=| b |
- Bangle between a , b is 0^ (or)
- Ca , b always form adjacent sides of a square.
- Da, b always form adjacent sides of a rectangle.
Correct answer
A. | a |=| b |
Step-by-step solution
Here, O A=| a |O D=A C=| b | aligned & In A B C, A B=| b | 2 & and B C=| b | 2 & In O B C , aligned aligned & = b 2 a+b 2 & 2 b a (1+ ^2 )+b (1- ^2 ) aligned aligned & [a+b+(a-b) ^2 -2 b ] =0 & (a-b) (1+ ^2 ) =0 & (a-b) ^2 =0 & a-b=0 | a |=| b | aligned