Consider the equation of the line $\vec r= -\hat i + 2\hat k + μ(4\hat i −\hat j + 2\hat k),$

Match List-I with List-II

Choose the correct answer from the options given below:

(A)-(III), (B)-(I), (C)-(IV), (D)-(II)

The correct answer is Option (4) → (A)-(III), (B)-(I), (C)-(IV), (D)-(II)

Given line: $\vec{r} = -\hat{i} + 2\hat{k} + \mu(4\hat{i} - \hat{j} + 2\hat{k})$

Compare with: $\vec{r} = \vec{a} + \mu \vec{b}$

• Point on the line (position vector) = $(-1, 0, 2)$
• Direction ratios = $(4, -1, 2)$
• Direction cosines = $\left( \frac{4}{\sqrt{21}}, \frac{-1}{\sqrt{21}}, \frac{2}{\sqrt{21}} \right)$
• Cartesian form: $\displaystyle \frac{x+1}{4} = \frac{y}{-1} = \frac{z-2}{2}$