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  4. If the foot of the perpendicular drawn from the point (1, 0,3) on a line passing through (α, 7, 1)is ((5/3), (7/3), (17/3)), then α is equal to . Given 5

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Q. If the foot of the perpendicular drawn from the point $(1, 0,3)$ on a line passing through $\left(\alpha, 7, 1\right)is \left(\frac{5}{3}, \frac{7}{3}, \frac{17}{3}\right)$, then $\alpha$ is equal to __________.
Given 5

JEE MainJEE Main 2020Three Dimensional Geometry

Solution:

$D.R.$ of $BP=< \frac{5}{3}-\alpha, \frac{7}{3}-7, \frac{17}{3}-1>$
$D.R.$ of $AP=< \frac{5}{3}-1, \frac{7}{3}-0, \frac{17}{3}-3>$
$BP\,\bot r\,AP$
$\Rightarrow \alpha=4$

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