1
MHT CET 2024 15th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

Let $\mathrm{L}_1: \frac{x+2}{5}=\frac{y-3}{2}=\frac{\mathrm{z}-6}{1}$ and $\mathrm{L}_2: \frac{x-3}{4}=\frac{y+2}{3}=\frac{z-3}{5}$ be the given lines. Then the unit vector perpendicular to both $\mathrm{L}_1$ and $\mathrm{L}_2$ is

A
$\frac{-\hat{i}-3 \hat{j}+\hat{k}}{11}$
B
$\frac{\hat{i}-3 \hat{j}+\hat{k}}{11}$
C
$\frac{\hat{i}+3 \hat{j}-\hat{k}}{11}$
D
$\frac{\hat{i}+3 \hat{j}+\hat{k}}{11}$
2
MHT CET 2024 15th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The perpendicular distance from the origin to the plane containing the two lines $\frac{x+2}{3}=\frac{y-2}{5}=\frac{z+5}{7}$ and $\frac{x-1}{1}=\frac{y-4}{4}=\frac{z+4}{7}$, is

A
$\frac{11}{\sqrt{6}}$ units
B
$11 \sqrt{6}$ units
C
$11$ units
D
$6 \sqrt{11}$ units
3
MHT CET 2024 15th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

Let $P(2,1,5)$ be a point in space and $Q$ be a point on the line $\bar{r}=(\hat{i}-\hat{j}+2 \hat{k})+\mu(-3 \hat{i}+\hat{j}+5 \hat{k})$. Then the value of $\mu$ for which the vector $\overline{\mathrm{PQ}}$ is parallel to the plane $3 x-y+4 z=1$ is

A
$\frac{-16}{13}$
B
$\frac{16}{13}$
C
$-\frac{13}{16}$
D
$\frac{13}{16}$
4
MHT CET 2024 15th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The centroid of tetrahedron with vertices $\mathrm{P}(5,-7,0), \mathrm{Q}(\mathrm{a}, 5,3), \mathrm{R}(4,-6, b)$ and $\mathrm{S}(6, \mathrm{c}, 2)$ is $(4,-3,2)$, then the value of $2 a+3 b+c$ is equal to

A
15
B
$-$7
C
7
D
$-$5
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