Match List-I with List-II

List-I (Straight Lines)	List-II (Direction Ratios)
(A) $\vec{r} = (\hat{i}+\hat{j}) + \lambda(2\hat{i}-\hat{j}+3\hat{k})$	(I) 2,1,-3
(B) $\frac{x}{2} = \frac{1-y}{-1} = \frac{z+1}{3}$	(II) -2,1,3
(C) $\frac{1-2x}{4} = \frac{y+1}{1} = \frac{2z+3}{6}$	(III) 2,-1,3
(D) $\vec{r} = (2\hat{i}-\hat{k}) + \lambda(2\hat{i}+\hat{j}-3\hat{k})$	(IV) 2,1,3

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The angle between the planes $2x + y + 3z - 2 = 0$ and $x - 2y + 5 = 0$ is :

If $\vec{a}$ and $\vec{b}$ are two perpendicular vector whose direction ratios are $(a_1,b_1,c_1)$ and $(a_2,b_2,c_2)$, then which of the following is a true statement?

A line passes through the point with position vector $2\hat{i} - \hat{j} + 4\hat{k}$ and is in the direction of the vector $\hat{i} + \hat{j} - 2\hat{k}$. The equation of the line in Cartesian form is:

If a line makes angles $\alpha$, $\beta$ and $\gamma$ with the positive directions of x-axis, y-axis and z-axis respectively, then $\sin^2\alpha + \sin^2\beta + \sin^2\gamma$ is equal to

Consider the lines $l_1: \frac{x-1}{0} = \frac{y-1}{1} = \frac{2-z}{1}$ and $l_2: \frac{x}{2} = \frac{y}{0} = \frac{2z-1}{4}$, then which of the following are correct?

(A) Direction Ratio's of $l_1 = <0, 1, 1>$

(B) Direction Ratio's of $l_2 = <2, 0, 2>$

(C) Angle between $l_1$ and $l_2 =$ $\frac{\pi}{3}$

(D) Angle between $l_1$ and $l_2 =$ $\frac{2\pi}{3}$

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Direction cosines of 2 lines are given by the equations $3l+m+5n=0, 6mn-2nl+5lm=0$ then which of the following statements are correct ?

(A) Direction ratios of two lines are (1, 2, -1) and (-2, 1, 1).

(B) Angle between lines is $\frac{\pi}{3}$.

(C) The angle between the lines is $\cos^{-1}\left(-\frac{1}{6}\right)$.

(D) Vectors parallel to these lines are $\hat i+2\hat j-\hat k$ and $-2\hat i+\hat j+\hat k$.

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