Let P be the image of the point (3, 1, 7) with respect to the plane x – y + z = 3. Then the equation of the plane passing through P and containing the straight line is

Engineering

Mathematics

Plane and Its Different Forms

Question

Let P be the image of the point (3, 1, 7) with respect to the plane x – y + z = 3. Then the equation of the plane passing through P and containing the straight line $\frac{x}{1} = \frac{y}{2} = \frac{z}{1}$ is

2x – y = 0

3x + z = 0

x – 4y + 7z = 0

x + y – 3z = 0

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Image of (3, 1, 7) in the plane x – y + z = 3 is $\frac{x - 3}{1} = \frac{y - 1}{- 1} = \frac{z - 7}{1} = - 2 (\frac{3 - 1 + 7 - 3}{1 + 1 + 1})$

x – 3 = – 4 ⇒ x = – 1

y – 1 = 4 ⇒ y = 5

z – 7 = – 4 ⇒ z = 3

(– 1, 5, 3)

Equation of the plane containing the line $\frac{x}{1} = \frac{y}{2} = \frac{z}{1}$ and passing through P is $| \begin{matrix} x & y & z \\ 1 & 2 & 1 \\ - 1 & 5 & 3 \end{matrix} | = 0$ .

x (6 – 5) – y (3 + 1) + z (5 + 2) = 0

⇒ x – 4y + 7z = 0.