First slide

Direction ratios and direction cosines

Question

The length of foot of perpendicular drawn from the point $P (- 3, - 4, 5)$ on $y - a x i s$

Moderate

A

$\sqrt{41}$
B

$\sqrt{34}$
C

5
D

none of these

Solution

We know that, in the $y - a x i s, x = 0$ and $z = 0$
Thus, foot of perpendicular from $P$ on $y - a x i s$ is $A (0, 4, 0)$ .
$∴ P A = \sqrt{{(0 - 3)}^{2} + {(4 - 4)}^{2} + {(0 - 5)}^{2}} = \sqrt{9 + 0 + 25} = \sqrt{34}$

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