You visited us 1 times! Enjoying our articles? Unlock Full Access!

Equation of a Plane : Intercept Form

Equation of t...

Question

Equation of the plane with intercepts $2$ , $3$ , $4$ on the $x$ , $y$ and $z$ axis respectively is

2 x + 3 y + 4 z = 1

No worries! We‘ve got your back. Try BYJU‘S free classes today!

2 x + 3 y + 4 z = 12

No worries! We‘ve got your back. Try BYJU‘S free classes today!

6 x + 4 y + 3 z = 1

No worries! We‘ve got your back. Try BYJU‘S free classes today!

6 x + 4 y + 3 z = 12

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D $6 x + 4 y + 3 z = 12$
The equation of plane with intercepts $a, b, c$ is given as $\frac{x}{a} + \frac{y}{b} + \frac{z}{c} = 1$

$\Rightarrow$ The equation of plane with intercepts $2, 3, 4$ is $\frac{x}{2} + \frac{y}{3} + \frac{z}{4} = 1$

$\Rightarrow 12 x + 8 y + 6 z = 24$

$\Rightarrow 6 x + 4 y + 3 z = 12$

Suggest Corrections

Similar questions

π

π

(2 x - 4 y + 3 z)

(x + 3 y - 4 z), (2 x + y - z)

(- 2 x + 3 y - z)

\frac{2}{x} - \frac{3}{y} + \frac{3}{z} = 10 \frac{1}{x} + \frac{1}{y} + \frac{1}{z} = 10 \frac{3}{x} - \frac{1}{y} + \frac{2}{z} = 13

\frac{2}{x} + \frac{3}{y} + \frac{10}{z} = 4, \frac{4}{x} - \frac{6}{y} + \frac{5}{z} = 1, \frac{6}{x} + \frac{9}{y} - \frac{20}{z} = 2; x, y, z \neq 0

2 x + 3 y - 4 z = 1

3 x - y + z + 2 = 0

4

x

2 x + 3 y - 4 z - 1 + λ (3 x - y + z + 2) = 0

λ

Join BYJU'S Learning Program