AP EAMCET202022 Sep 2020Evening ShiftMathematicsThree Dimensional GeometryActual
Find the angle between the diagonals of parallelogram P Q R S , if P Q =3 i -2 j +2 k and P S = i -2 k
Options
- AOnly =- 3 10
- BBoth = 3 10
- C=- 3 10
- D=- 11 10
Correct answer
A. Only =- 3 10
Step-by-step solution
60. (a) aligned P Q & =3 i -2 j +2 k P S & = i -2 k aligned aligned & Eqs. (i) + (ii) P Q + P S =4 i -2 j + 0 k & P R =4 i -2 j & Eqs. (i) - (ii) P Q - P S =2 i -2 j +4 k & - Q S = 2 i -2 j +4 k & Q S =-2 i +2 j -4 k & aligned Let be the angle between diagonal P R and Q S aligned & = P R Q S | P R || Q S | & = (4 i -2 j )(-2 i +2 j -4 k ) 16+4 4+4+16 & = -8-4 20 24 = -12 2 5 2 6 & = -3 30 =- 9 30 =- 3 10 & =- 3 10 aligned Hence, option (1) is correct.