CBSE 2022 · Region 1 · Set 3 · Q8 · 3 marks
Find the co-ordinates of point where the line $\displaystyle \frac{x-3}{-1}=\frac{\mathrm{y}+4}{1}=\frac{\mathrm{z}+5}{6}$ crosses the plane passing through points $\displaystyle \left(\frac{7}{2}, 0,0\right),(0,7,0)$ and ($\displaystyle 0$, $\displaystyle 0$, $\displaystyle 7$).
Marking-scheme solution
Let the coordinates of required point on line is \(\displaystyle (-\lambda+3, \lambda-4,6 \lambda-5)\) for some \(\displaystyle \lambda\) Equation of plane is \(\displaystyle \frac{2 x}{7}+\frac{y}{7}+\frac{z}{7}=1\)
\[\therefore 2(-\lambda+3)+\lambda-4+6 \lambda-5=7
\]
Gives \(\displaystyle 5 \lambda=10\) i.e. \(\displaystyle \lambda=2\)
∴ Required point is ($\displaystyle 1$, -$\displaystyle 2$, $\displaystyle 7$)
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CBSE Class 12 Mathematics past-paper question from the 2022board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.