JEE Advanced · Mathematics · 31. 3D Geometry

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

A $x + y - 3 z = 0$
B $3 x + z = 0$
C $x - 4 y + 7 z = 0$
D $2 x - y = 0$

Verified Solution

Answer & Solution

Correct Answer

(C) $x - 4 y + 7 z = 0$

Step-by-step Solution

Detailed explanation

Let

F

be mid point of

AP

Line

AP : \frac{x - 3}{1} = \frac{y - 1}{- 1} = \frac{z - 7}{1} = λ

\Rightarrow F (3 + λ, 1 - λ, λ + 7)

lies in the plane

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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From JEE Advanced

Consider the Bohr's model of a one-electron atom where the electron moves around the nucleus. In the following List-I contains some quantities for the

n^{t h}

orbit of the atom and List-II contains options showing how they depend on

n

List - I	List - II
(I) Radius of the $n^{t h}$ orbit	$(P)$ $\propto n^{- 2}$
(II) Angular momentum of the electron in the $n^{t h}$ orbit	$(Q)$ $\propto n^{- 1}$
(III) Kinetic energy of the electron in the $n^{t h}$ orbit	$(R)$ $\propto n^{0}$
(IV) Potential energy of the electron in the $n^{t h}$ orbit	$(S)$ $\propto n^{1}$
	$(T)$ $\propto n^{2}$
	$(U)$ $\propto n^{1 / 2}$

Which of the following options has the correct combination considering List-I and List-II?

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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 x1=y2=z1 is

Step-by-step Solution

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