1
MHT CET 2024 4th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The co-ordinates of the point where the line through $\mathrm{A}(3,4,1)$ and $\mathrm{B}(5,1,6)$ crosses the $x y$-plane are

A
$\left(\frac{13}{5}, \frac{23}{5}, 0\right)$
B
$\left(-\frac{13}{5}, \frac{23}{5}, 0\right)$
C
$\left(\frac{13}{5},-\frac{23}{5}, 0\right)$
D
$\left(-\frac{13}{5},-\frac{23}{5}, 0\right)$
2
MHT CET 2024 4th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The Cartesian equation of a line is $2 x-2=3 y+1=6 z-2$, then the vector equation of the line is

A
$\overline{\mathrm{r}}=\left(\hat{\mathrm{i}}-\frac{\hat{\mathrm{j}}}{3}+\frac{\hat{\mathrm{k}}}{3}\right)+\lambda(3 \hat{\mathrm{i}}+2 \hat{\mathrm{j}}+\hat{\mathrm{k}})$
B
$\overline{\mathrm{r}}=\left(-\hat{\mathrm{i}}+\frac{\hat{\mathrm{j}}}{3}-\frac{\hat{\mathrm{k}}}{3}\right)+\lambda\left(\frac{1}{2} \hat{\mathrm{i}}+\frac{1}{3} \hat{\mathrm{j}}+\frac{1}{6} \hat{\mathrm{k}}\right)$
C
$\overline{\mathrm{r}}=(3 \hat{\mathrm{i}}-\hat{\mathrm{j}}-\hat{\mathrm{k}})+\lambda(3 \hat{\mathrm{i}}+2 \hat{\mathrm{j}}+\hat{\mathrm{k}})$
D
$\overline{\mathrm{r}}=(\hat{\mathrm{i}}-\hat{\mathrm{j}}+\hat{\mathrm{k}})+\lambda\left(\frac{1}{2} \hat{\mathrm{i}}+\frac{1}{3} \hat{\mathrm{j}}+\frac{1}{6} \hat{\mathrm{k}}\right)$
3
MHT CET 2024 4th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The lines $\frac{x-2}{1}=\frac{y-3}{1}=\frac{z-4}{-k} \quad$ and $\frac{x-1}{\mathrm{k}}=\frac{y-4}{2}=\frac{\mathrm{z}-5}{1}$ are coplanar if

A
$\mathrm{k}=1$ or $\mathrm{k}=-1$
B
$\mathrm{k}=0$ or $\mathrm{k}=-3$
C
$\mathrm{k}=3$ or $\mathrm{k}=-3$
D
$\mathrm{k}=0$ or $\mathrm{k}=3$
4
MHT CET 2024 4th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

Let $\mathrm{L}_1: \frac{x+1}{3}=\frac{y+2}{1}=\frac{z+1}{2}$ and $\mathrm{L}_2: \frac{x-2}{1}=\frac{y+2}{2}=\frac{z-3}{3}$ be two given lines. Then the unit vector perpendicular to $L_1$ and $L_2$ is

A
$\frac{-\hat{\mathrm{i}}+7 \hat{\mathrm{j}}+7 \hat{\mathrm{k}}}{\sqrt{99}}$
B
$\frac{-\hat{\mathrm{i}}-7 \hat{\mathrm{j}}+5 \hat{\mathrm{k}}}{5 \sqrt{3}}$
C
$\frac{-\hat{i}+7 \hat{j}+5 \hat{k}}{5 \sqrt{3}}$
D
$\frac{7 \hat{\mathrm{i}}-7 \hat{\mathrm{j}}-7 \hat{\mathrm{k}}}{\sqrt{99}}$
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