Let the line passing through the points $(-1,2,1)$ and parallel to the line $\frac{x-1}2=\frac{y+1}3=\frac z4$ intersect the line $\frac{x+2}3=\frac{y-3}2=\frac{z-4}1$ at the point $P$. Then the distance of $P$ from the point $Q(4,-5,1)$ is

Question

Dr. Abubacker · Accepted Answer

[Solution by Dr. Abubacker] Line 1: $(-1+2s,\,2+3s,\,1+4s)$; Line 2: $(-2+3t,\,3+2t,\,4+t)$. Equating coordinates gives $s=t=1$, so $P=(1,5,5)$. $PQ=\sqrt{3^2+10^2+4^2}=\sqrt{125}=5\sqrt5$. Answer (2).

Q. Let the line passing through the points $(-1,2,1)$ and parallel to the line $\frac{x-1}2=\frac{y+1}3=\frac z4$ intersect the line $\frac{x+2}3=\frac{y-3}2=\frac{z-4}1$ at the point $P$. Then the distance of $P$ from the point $Q(4,-5,1)$ is

Explanation

Reviewed by Dr. Abubacker

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