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  4. The distance of the point having position vector - hati + 2 hatj + 6 hatk from the straight line passing through the point (2, 3, -4) and parallel to the vector, 6 hati + 3 hatj - 4 hatk is :

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Q. The distance of the point having position vector $- \hat{i} + 2\hat{j} + 6 \hat{k}$ from the straight line passing through the point $(2, 3, -4)$ and parallel to the vector, $6 \hat{i} + 3 \hat{j} - 4 \hat{k} $ is :

JEE MainJEE Main 2019Three Dimensional Geometry

Solution:

$AD = \left|\frac{\overrightarrow{AP} . \vec{n}}{\left|\vec{n}\right|}\right| = \sqrt{61} $
$ \Rightarrow PD = \sqrt{AP^{2} -AD^{2}} = \sqrt{110-61} = 7 $

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