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JEE MAIN Mathematics QUESTION #965
Question 1
Let a line pass through two distinct points \(P(-2,-1,3)\) and \(Q\), and be parallel to the vector \(3\hat{i}+2\hat{j}+2\hat{k}\). If the distance of the point \(Q\) from the point \(R(1,3,3)\) is 5, then the square of the area of \(\triangle PQR\) is equal to:
  • 148
  • 136
  • 144
  • 140✔️
Correct Answer Explanation
The line through \(P\) parallel to \(\vec{v}=3\hat{i}+2\hat{j}+2\hat{k}\) gives \(Q = P + t\vec{v}\). Using \(|QR|=5\) to find \(t\), then computing \(\text{Area}^2 = \frac{1}{2}|\vec{PQ}\times\vec{PR}|^2\) yields 140.