99 Percentile Qs Bank for JEE MainMathematicsVector Algebra

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

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