Question:medium
Let \( PQR \) be a triangle such that
\[
\vec{PQ}=-2\hat i-\hat j+2\hat k,\quad
\vec{PR}=a\hat i+b\hat j-4\hat k,\ a,b\in\mathbb{Z}.
\]
Let \( S \) be the point on \( QR \) which is equidistant from the lines \( PQ \) and \( PR \).
If
\[
|\vec{PR}|=9 \quad \text{and} \quad \vec{PS}=\hat i-7\hat j+2\hat k,
\]
then the value of \( 3a-4b \) is:
Let \( PQR \) be a triangle such that
\[
\vec{PQ}=-2\hat i-\hat j+2\hat k,\quad
\vec{PR}=a\hat i+b\hat j-4\hat k,\ a,b\in\mathbb{Z}.
\]
Let \( S \) be the point on \( QR \) which is equidistant from the lines \( PQ \) and \( PR \).
If
\[
|\vec{PR}|=9 \quad \text{and} \quad \vec{PS}=\hat i-7\hat j+2\hat k,
\]
then the value of \( 3a-4b \) is:
Show Hint
For equidistance from two lines through a point, always apply the angle-bisector condition using direction vectors.
Updated On: Feb 24, 2026
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Correct Answer: 29
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