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Mathematics · 2022 · 4 marks
CBSE 2022 · Region 2 · Set 3 · Q13
Find the coordinates of the point where the line through (5, 1, 6) and (3, 4, 1) crosses the zx-plane. Case-Study Based Question
Find the coordinates of the point where the line through ($\displaystyle 5$, $\displaystyle 1$, $\displaystyle 6$) and ($\displaystyle 3$, $\displaystyle 4$, $\displaystyle 1$) crosses the zx-plane. Case-Study Based Question
Marking-scheme solution
Equations of line
\[\frac{x-5}{-2}=\frac{y-1}{3}=\frac{z-6}{-5}
\]
Any point on the line
\[(-2 \lambda+5,3 \lambda+1,-5 \lambda+6)
\]
The point lies on ZX- plane i.e., \(\displaystyle y=0\)
\[\therefore 3 \lambda+1=0
\]
\(\displaystyle \lambda=-\frac{1}{3}\)
∴ Point is \(\displaystyle \left(\frac{17}{3}, 0, \frac{23}{3}\right)\)
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CBSE Class 12 Mathematics past-paper question from the 2022 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.