The length of the perpendicular drawn from (1, 2, 3) to the line $\frac{x - 6}{3} = \frac{y - 7}{2} = \frac{\mathcal{z}–7}{- 2}$ is

Question

Dr. Abubacker · Accepted Answer

(d)
Let $P$ be the point ($1,\ 2,\ 3$) and $PN$ be the length of the perpendicular from $P$ on the given line
Coordinates of point $N$ are $(3\lambda + 6,\ 2\lambda + 7,\  - 2\lambda + 7)$
Now $PN$ is perpendicular to the given line or vector $3\widehat{i} + 2\widehat{j} - 2\widehat{k}$
$\Rightarrow 3(3\lambda + 6 - 1) + 2(2\lambda + 7 - 2) - 2( - 2\lambda + 7 - 3) = 0$
$\Rightarrow \ \lambda = - 1$
Then, point $N$ is (3, 5, 9)
$\Rightarrow PN = 7$

Q. The length of the perpendicular drawn from (1, 2, 3) to the line $\frac{x - 6}{3} = \frac{y - 7}{2} = \frac{\mathcal{z}–7}{- 2}$ is

Explanation

Reviewed by Dr. Abubacker

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