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Previous Year Question (PYQs)
2
The perpendicular distance of the point $P(1,2,3)$ from the line $\dfrac{x-6}{3}=\dfrac{y-7}{2}=\dfrac{z-7}{-2}$ is
Solution
Line passes through $A(6,7,7)$ with direction $\vec v=\langle3,2,-2\rangle$.
$\vec{AP}=\langle-5,-5,-4\rangle$. Distance $=\dfrac{\lVert \vec{AP}\times\vec v\rVert}{\lVert\vec v\rVert}=\dfrac{\sqrt{833}}{\sqrt{17}}=\sqrt{49}=7$.
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