KCET2020MathematicsThree Dimensional Geometry
If a and b are unit vectors and is the angle between a and b , then 2 is equal to
Options
- A| a + b |
- B| a + b | 2
- C| a - b | 2
- D| a - b |
Correct answer
C. | a - b | 2
Step-by-step solution
Given a and b are unit vectors | a |=1 and | b |=1 We know that, | a - b |²=( a - b ) ( a - b )=| a |²-2 a b +| b |²=| a |²-2| a || b | +| b |²=1-2 1 1 +1=2-2 | a - b |²=2(1- )=2 (2 ² / 2 )=4 ² / 2 array ll & ² 2 = 1 4 | a - b | & 2 = 1 2 | a - b | array