AP EAMCET20228 Jul 2022Evening ShiftMathematicsVector AlgebraActual
If the points P = i +2 j , Q =4 i +6 j , R =5 i +7 j , S =a i +b j are the consecutive vertices of a parallelogram P Q R S , then
Options
- Aa=2, b=4
- Ba=3, b=4
- Ca=2, b=3
- Da=3, b=5
Correct answer
C. a=2, b=3
Step-by-step solution
Given, aligned & P = i +2 j & Q =4 i +6 j & R =5 i +7 j & S =a i +b j aligned Let A be the point of intersection of diagonals P R and Q S . A is the mid-point of P R and Q S both. Now, A= ( 1+5 2 , 2+7 2 ) (3, 9 2 )[ A is the mid-point of P R] Also, A ( 4+a 2 , 6+b 2 ) (3, 9 2 ) 4+a 2 =3 a=2 and 6+b 2 = 9 2 b=3 Thus, (a, b) (2,3)