CUET Mathematics - The direction ratios of the line perpendicular to the lines x-5/-3 = y+11/-3 = z+3/1 and x-7/1 = y+2/-2 = z-4/-1 are proportional to: | PYQs + Solutions

14 May Shift 1

Consider the line $\vec{r} = \hat{i} - 2\hat{j} + 4\hat{k} + \lambda(-\hat{i} + 2\hat{j} - 4\hat{k})$

Match List-I with List-II

List-I	List-II
(A) A point on the given line	(I) $\left(\frac{-1}{\sqrt{21}}, \frac{2}{\sqrt{21}}, \frac{-4}{\sqrt{21}}\right)$
(B) direction ratios of the line	(II) $(4, -2, -2)$
(C) direction cosines of the line	(III) $(1, -2, 4)$
(D) direction ratios of a line perpendicular to given line	(IV) $(-1, 2, -4)$

Choose the correct answer from the options given below:

14 May Shift 2

Consider a line $\vec{r} = (\hat{i} + 4\hat{j}) + \lambda(2\hat{i} - 2\hat{j} + 3\hat{k})$ , then which of the following statements are correct?

(A) it passes through point (9, -4, 12)

(B) it passes through point (1, 4, -1)

(C) its direction cosine's are $\frac{2}{\sqrt{17}}, \frac{-2}{\sqrt{17}}, \frac{3}{\sqrt{17}}$

(D) its Cartesian equation is $\frac{x - 1}{2} = \frac{y - 4}{-2} = \frac{z}{3}$

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26 May Shift 2

If the points (-1, -1, 2), (2, m, 5) and (3, 11, 6) are collinear, then m equals

CUET Mathematics 2025 3 June Shift 2 PYQs