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Mathematics · 2026 · 2 marks
CBSE 2026 · Region 2 · Set 3 · Q21
Find the co-ordinates of the point on line x=(y -1)/2=(z -2)/3 whose y co- ordinate is 3 times the x co-ordinate.
Find the co-ordinates of the point on line $\displaystyle x=\frac{\mathrm{y}-1}{2}=\frac{\mathrm{z}-2}{3}$ whose y co- ordinate is $\displaystyle 3$ times the $\displaystyle x$ co-ordinate.
Marking-scheme solution
Let $\displaystyle x=\dfrac{y-1}{2}=\dfrac{z-2}{3}=\lambda$
The coordinates of any point on this line is $\displaystyle A(\lambda, 2 \lambda+1,3 \lambda+2)$
According to question, $\displaystyle 2 \lambda+1=3 \lambda \Rightarrow \lambda=1$
$\displaystyle \therefore$ The required point is $\displaystyle A(1,3,5)$.
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CBSE Class 12 Mathematics past-paper question from the 2026 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.