Question
Question: The equation to the plane through the point (2, 3, 1) and (4, – 5, 3) & parallel to x-axis is :...
The equation to the plane through the point (2, 3, 1) and
(4, – 5, 3) & parallel to x-axis is :
A
x + y + 4z = 7
B
x + 4z = 7
C
x – 4z = 7
D
y + 4z = 7
Answer
y + 4z = 7
Explanation
Solution
Any plane through point A(2, 3, 1) is
Ž a(x – 2) + b(y – 3) + c(z – 1) = 0.......(i)
It passes through point B(4, –5, 3)
Then, a(4 – 2) + b(–5 –3) + c(3 – 1) = 0
Ž 2a – 8b + 2c = 0
Ž a – 4b + c = 0 .........(ii)
Q plane (i) is parallel to x-axis whose DC's are
1, 0, 0
Then , a(1) + b(0) + c(0) = 0 .........(iii)
By (ii) and (iii)
Ž find the values of a, b and c & put in equation (i)