AP EAMCET · Maths · Three Dimensional Geometry

If $x$ -coordinate of a point $P$ on the line joining the points $Q (2, 2, 1)$ and $R (5, 2, - 2)$ is $4$ , then the $y$ -coordinate of $P =$

A $- \frac{1}{2}$ ( $x$ -coordinate of $P$ )
B $- 2$ ( $z$ -coordinate of $P$ )
C $2$ ( $z$ -coordinate of $P$ )
D Sum of $x$ and $z$ coordinates of $P$

Verified Solution

Answer & Solution

Correct Answer

(B) $- 2$ ( $z$ -coordinate of $P$ )

Step-by-step Solution

Detailed explanation

Given, x-coordinate of a point P on the line joining the points Q2,2,1 and R5,2,-2 is 4, Now let assume that point P is dividing the point Q & R in ratio of λ:1, So by section formula we get, 4=2+λ×5λ+1…

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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If x-coordinate of a point P on the line joining the points Q2,2,1 and R5,2,-2 is 4, then the y-coordinate of P=

Step-by-step Solution

If $x$ -coordinate of a point $P$ on the line joining the points $Q (2, 2, 1)$ and $R (5, 2, - 2)$ is $4$ , then the $y$ -coordinate of $P =$