The x-intercept of a plane π passing through the point 1,1,1 is 52 and the perpendicular distance from the origin to the plane π is 57. If the y-intercept of the plane π is negative and the z-intercept is positive then its y-intercept is

AP EAMCET · Maths · Three Dimensional Geometry

The $x$ -intercept of a plane $π$ passing through the point $(1, 1, 1)$ is $\frac{5}{2}$ and the perpendicular distance from the origin to the plane $π$ is $\frac{5}{7}$ . If the $y$ -intercept of the plane $π$ is negative and the $z$ -intercept is positive then its $y$ -intercept is

A $- \frac{5}{3}$
B $- \frac{5}{6}$
C $- \frac{3}{2}$
D $- \frac{5}{2}$

Verified Solution

Answer & Solution

Correct Answer

(A) $- \frac{5}{3}$

Step-by-step Solution

Detailed explanation

Let the equation of plane be xa+yb+zc=1 Now given a=52 So, equation becomes 2x5+yb+zc=1 Now given plane passes through 1,1,1 ⇒25+1b+1c=1 ⇒1b+1c=35 Now given distance from origin is 57 So by formula we get, 1425+1b2+1c2=57 ⇒425+1b+1c2-2bc=75 Now using value of…

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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