MHT CET202520 Apr 2025Evening ShiftMathematicsVector AlgebraActual
If a and b are unit vectors and is the angle between them, then / 2=
Options
- A| a - b |
- B| a + b |
- C| a + b | | a - b |
- D| a - b | | a + b |
Correct answer
D. | a - b | | a + b |
Step-by-step solution
Given that a and b are unit vectors, with angle between them, their dot product yields a b = . Evaluating | a - b |^2 using vector algebra: | a - b |^2 = 2(1 - ) = 4 ^2( /2) Hence, | a - b | = 2 ( /2) for [0, ] . Similarly for | a + b |^2 : | a + b |^2 = 2(1 + ) = 4 ^2( /2) Thus, | a + b | = 2 ( /2) . Taking the ratio yields the tangent of the half-angle: ( /2) = | a - b | | a + b | This result corresponds to option D .