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Find the perpendicular distance of the points (2,3,4) from the line \( \large\frac{4-x}{2}=\frac{y}{6}=\frac{1-z}{3}\), Also, find the coordinates of the foot of the perpendicular.

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  • Distance between two points is $\sqrt {(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}$
Step 1:
The given line $l$ is
Any point on $Q$ on the line $l$ is given by
Step 2:
Direction ratios of PQ are
Or $-2\lambda+2,6\lambda-3,-3\lambda-3$
Since $PQ\perp l$
$\Rightarrow 49\lambda-13=0$
$\Rightarrow \lambda=\large\frac{13}{49}$
Step 3:
Hence the coordinates of $Q$ are
Step 4:
The distance PQ is given by
On simplifying we get,
$\Rightarrow 4$units
answered Oct 2, 2013 by sreemathi.v

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