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Mathematics · 2023 · 2 marks
CBSE 2023 · Region 5 · Set 1 · Q25
Find the vector and the cartesian equations of a line that passes through the point A (1,2,-1) and parallel to the line 5 x-25=14-7 y =35 z.
Find the vector and the cartesian equations of a line that passes through the point $\displaystyle \mathrm{A}(1,2,-1)$ and parallel to the line $\displaystyle 5 x-25=14-7 \mathrm{y}=35 \mathrm{z}$.
Marking-scheme solution
The given line is
$$\frac{x-5}{\dfrac{1}{5}}=\frac{\mathrm{y}-2}{-\dfrac{1}{7}}=\frac{\mathrm{z}}{\dfrac{1}{35}}, \text { or } \frac{x-5}{7}=\frac{\mathrm{y}-2}{-5}=\frac{\mathrm{z}}{1}
$$
So, the required vector equation of the line passing through $\displaystyle (1,2,-1)$ is
$$\vec{r}=(\hat{\imath}+2 \hat{\jmath}-\hat{k})+\lambda(7 \hat{\imath}-5 \hat{\jmath}+\hat{k})
$$
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CBSE Class 12 Mathematics past-paper question from the 2023 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.