First slide

Direction ratios and direction cosines

Question

The perpendicular bisector of the line segment with end points $(2, 3, 2)$ and $(- 4, 1, 4)$ passes through the point $(- 3, 6, 1)$ and has equation of the form $\frac{x + 3}{a} = \frac{y - 6}{b} = \frac{z - 1}{c}$ where $a, b, c$ are relatively prime integers with $a > 0$ , then the value of $a b c - (a + b + c)$ is

Moderate

A

$- 1$
B

$- 2$
C

$- 3$
D

$- 4$

Solution

The midpoint of the line segment joining $(2, 3, 2)$ , $(- 4, 1, 4)$ is $(\frac{2 - 4}{2}, \frac{3 + 1}{2}, \frac{2 + 4}{2}) = (- 1, 2, 3)$
Given that the perpendicular bisector is passing through the point $(- 3, 6, 1)$ also
Hence the equation of the perpendicular bisector is $\frac{x + 3}{- 1 + 3} = \frac{y - 6}{2 - 6} = \frac{z - 1}{3 - 1}$
Rewrite the above equation as $\frac{x + 3}{- 1 + 3} = \frac{y - 6}{2 - 6} = \frac{z - 1}{3 - 1}$
Comparing this with the given line $a = 1, b = - 2, c = 1$
Consider the expression $a b c - (a + b + c) = - 2 - 0 = - 2$

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