Question
Question: The equation of the plane passes through (2, 3, 4) and parallel to the plane x + 2y + 4z = 5 is -...
The equation of the plane passes through
(2, 3, 4) and parallel to the plane x + 2y + 4z = 5 is -
A
x + 2y + 4z = 10
B
x + 2y + 4z = 3
C
x + 2y + 4z = 24
D
x + 2y + 4z = 2
Answer
x + 2y + 4z = 24
Explanation
Solution
& x + 2y + 4z = 5 \\
& a,b,c \Rightarrow 1,2,4\mspace{6mu}
\end{aligned} \right.\ $$
<img src="https://cdn.pureessence.tech/canvas_502.png?top_left_x=1200&top_left_y=0&width=300&height=33" style="width:1.85417in;height:0.20833in" />P(2, 3, 4) = (x<sub>1</sub>, y<sub>1</sub>, z<sub>1</sub>)
Eq. of the plane is
Ž a (x – x<sub>1</sub>) + b(y – y<sub>1</sub>) + c (z – z<sub>1</sub>) = 0