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

The vector equation of the plane through the line of intersection of the planes $x+y+z=1$ and $2 x+3 y+4 z=5$, which is perpendicular to the plane $x-y+z=0$, is

A
$\overline{\mathrm{r}} \cdot(\hat{\mathrm{i}}-\hat{\mathrm{k}})=2$
B
$\overline{\mathrm{r}} \cdot(\hat{\mathrm{i}}+\hat{\mathrm{k}})+2=0$
C
$\overline{\mathrm{r}} \cdot(\hat{\mathrm{i}}+\hat{\mathrm{k}})=2$
D
$\overline{\mathrm{r}} \cdot(\hat{\mathrm{i}}-\hat{\mathrm{k}})+2=0$
2
MHT CET 2024 15th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The equation of a line passing through the point $(2,-1,1)$ and parallel to the line joining the points $\hat{i}+2 \hat{j}+2 \hat{k}$ and $-\hat{i}+4 \hat{j}+\hat{k}$ is

A
$\bar{r}=(2 \hat{i}-\hat{j}+\hat{k})+\lambda(-2 \hat{i}+2 \hat{j}-\hat{k})$
B
$\bar{r}=(2 \hat{i}-\hat{j}+\hat{k})+\lambda(2 \hat{i}+6 \hat{j}+3 \hat{k})$
C
$\bar{r}=(2 \hat{i}-\hat{j}+\hat{k})+\lambda(2 \hat{i}-2 \hat{j}-\hat{k})$
D
$\overline{\mathrm{r}}=(2 \hat{\mathrm{i}}-\hat{\mathrm{j}}+\hat{\mathrm{k}})+\lambda(2 \hat{\mathrm{i}}-6 \hat{\mathrm{j}}-3 \hat{\mathrm{k}})$
3
MHT CET 2024 15th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The foot of the perpendicular drawn from origin to a plane is $\mathrm{M}(2,1,-2)$, then vector equation of the plane is

A
$\overline{\mathrm{r}} \cdot(2 \hat{\mathrm{i}}+\hat{\mathrm{j}}-2 \hat{\mathrm{k}})=9$
B
$\overline{\mathrm{r}} \cdot(-2 \hat{\mathrm{i}}-\hat{\mathrm{j}}-2 \hat{\mathrm{k}})=7$
C
$\bar{r} \cdot(2 \hat{i}-\hat{j}-2 \hat{k})=9$
D
$\overline{\mathrm{r}} \cdot(2 \hat{\mathrm{i}}-\hat{\mathrm{j}}-\hat{\mathrm{k}})=7$
4
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
$\frac{\hat{i}+3 \hat{j}+\hat{k}}{11}$
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