AP EAMCET202418 May 2024Morning ShiftMathematicsVector AlgebraActual
If f , g , h mutually orthogonal vectors of equal magnitudes, then the angle between the vectors f + g + h and h is
Options
- A⁻¹ ( 3 4 )
- B⁻¹ ( 1 3 )
- C- ⁻¹ ( 1 3 )
- D- ⁻¹ ( 3 4 )
Correct answer
B. ⁻¹ ( 1 3 )
Step-by-step solution
Given, f , g and h are mutually orthogonal vector So, f g = g h = f h =0 . Let, | f |=| g |=| h |=k Now, ( f + g + h ) h =| f + g + h | h | | h |^2=| f + g + h | h | = | h | | f + g + h | (i) aligned & Since, | f + g + h |^2=| f |^2+| g |^2+| h |^2+0+0+0 & | f + g + h |= k^2+k^2+k^2 = 3 k aligned By ( i ), = k 3 k = ⁻¹ ( 1 3 )