CBSE Class 12 Mathematics 2024: question 25

Hints

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Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

1. Let the line make angle α with each axis, so $l=m=n=\cos \alpha$. Using $l^2+m^2+n^2=1$: $3l^2=1\Rightarrow l=\frac{1}{\sqrt{3}}$ (taking the positive value; the negative value gives the same line).

   1 mark

2. Direction cosines are $\frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}}$, so direction ratios are $1,1,1$.

   ½ mark

3. Vector equation: $\vec{r}=(2\hat{i}+3\hat{j}-5\hat{k})+\lambda (\hat{i}+\hat{j}+\hat{k})$.

   ½ mark

Answer: $\vec{r}=2\hat{i}+3\hat{j}-5\hat{k}+\lambda (\hat{i}+\hat{j}+\hat{k})$

Revise the chapter

• Chapter: Three Dimensional Geometry (notes, formulas, where marks are lost and every past question)
• Topic: Equation of a Line in Space