Let a and b are two vectors of magnitude 4 inclined at an angle 3 , then what is the angle between a and a - b ?

Step-by-step solution

The angle between a and a - b is given by = a ( a - b ) | a || a - b | Now, a ( a - b )= a a - a b a a =| a |^2 Given that magnitude of a and b is 4 aligned | a |=| b | & =4 | a |^2 & =4^2=16 aligned and a b =| a | b | 3 =4 4 1 2 =8 aligned | a - b |^2 & =| a |^2+| b |^2- a b - b a & =16+16-8-8=16 & = 16-8 4 16 = 8 4 4 = 1 2 = 3 aligned = 3