Ques. 1JEE Main 2025, 23 January (Evening Shift)
Let the point A divide the line segment joining the points P(-1,-1,2) and Q(5,5,10) internally in the ratio r:1 (r>0). If O is the origin and ( OQ OA )- 15 | OP OA |2=10, then the value of r is :
- 7
- 14
- 7
- 3
Answer
(3) 7
Solution
A divides PQ in r:1: OA= OP+r OQr+1
[figure]
OQ OA= 10+150rr+1 and OP OA= rr+1( OP OQ), with OP OQ=(-20,20,0), | |2=800
10+150rr+1- 160r2(r+1)2=10 20r2-140r=0
r=7
Answer: (3)