AP EAMCET · Maths · Three Dimensional Geometry

$X$ intercept of the plane containing the line of intersection of the planes $x - 2 y + z + 2 = 0$ and $3 x - y - z + 1 = 0$ and also passing through $(1, 1, 1)$ is

A $\frac{1}{3}$
B $2$
C $\frac{1}{2}$
D $\frac{1}{4}$

Verified Solution

Answer & Solution

Correct Answer

(C) $\frac{1}{2}$

Step-by-step Solution

Detailed explanation

Equation of plane passing through line of intersection of given planes is given by, x-2y+z+2+α3x-y-z+1=0 Since, the plane passes through the point 1, 1, 1 therefore, this point will satisfy equation of plane. ⇒1-2+1+2+α3-1-1+1=0 ⇒α=-1 Then,…

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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X intercept of the plane containing the line of intersection of the planes x-2y+z+2=0 and 3x-y-z+1=0 and also passing through (1,1,1) is

Step-by-step Solution

$X$ intercept of the plane containing the line of intersection of the planes $x - 2 y + z + 2 = 0$ and $3 x - y - z + 1 = 0$ and also passing through $(1, 1, 1)$ is