First slide

Straight lines in 3D

Question

The perpendicular distance of $P (1, 2, 3)$ from the line $\frac{x - 6}{3} = \frac{y - 7}{2} = \frac{z - 7}{- 2}$ is

Moderate

A

7
B

5
C

0
D

none of these

Solution

The point $A (6, 7, 7)$ is on the lien. Let the perpendicular from $P$ meet the line in $L .$ Then

$A P^{2} = {(6 - 1)}^{2} + {(7 - 2)}^{2} + {(7 - 3)}^{2} = 66.$

Also $A L =$ projection of $A P$ on line $(a c t u a l d . c .' s \frac{3}{\sqrt{17}}, \frac{2}{\sqrt{17}}, \frac{- 2}{\sqrt{17}})$

$= (6 - 7) . \frac{3}{\sqrt{17}} + (7 - 2) . \frac{2}{\sqrt{17}} + (7 - 3) . \frac{- 2}{\sqrt{17}}$

$= \sqrt{17} .$

$∴ ⊥$ distance $d$ of $P$ from the line is given by $d^{2} = A P^{2} - A L^{2} = 66 - 17 = 49,$ so that $d = 7$ .

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App