CUET Mathematics - Distance between the point (3, 4, 5) and the point where the line x-3/1 = y-4/2 = z-5/2 meets the plane x + y + z = 17 is : | PYQs + Solutions

CUET Mathematics 2023 22 May Shift 3

Geometry

Medium

$\frac{3}{2}$

✅ Correct Option: 3

Related questions:

16 May Shift 1

The angle between the pair of lines given by $\vec{r} = \hat{i} + 2\hat{j} - 3\hat{k} + \lambda (\hat{i} - 2\hat{j} + 2\hat{k})$ and $\vec{r} = 5\hat{i} + \hat{j} + \hat{k} + \mu (3\hat{i} - 2\hat{j} + 6\hat{k})$ is

23 May Shift 3

Match List I with List II

LIST I	LIST II
A. $lx + my + nz = d$ is	I. Equation of plane passing through a given point and normal to given vector
B. $\frac{x}{a} + \frac{y}{b} + \frac{z}{c} = 1$ is	II. Equation of plane in normal form
C. $(\vec{r} - \vec{a}) \cdot \vec{n} = 0$	III. Plane passing through the intersection of two planes
D. $(a_1x + b_1y + c_1z + d_1) + \lambda(a_2x + b_2y + c_2z + d_2) = 0$	IV. Intercept from of plane

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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) $(-1, 2, -4)$

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CUET Mathematics 2023 22 May Shift 3 PYQs

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