MHT CET 2024 2nd May Evening Shift | Three Dimensional Geometry Question 66 | Mathematics

The equation of the line, through $\mathrm{A}(1,2,3)$ and perpendicular to the vector $2 \hat{\mathrm{i}}+\hat{\mathrm{j}}-\hat{\mathrm{k}}$ and $\hat{i}+3 \hat{j}+2 \hat{k}$, is

$\overline{\mathrm{r}}=(\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+3 \hat{\mathrm{k}})+\lambda(\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}})$

$\overline{\mathrm{r}}=(\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+3 \hat{\mathrm{k}})+\lambda(\hat{\mathrm{i}}-\hat{\mathrm{j}}-\hat{\mathrm{k}})$

$\overline{\mathrm{r}}=(\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+3 \hat{\mathrm{k}})+\lambda(\hat{\mathrm{i}}+\hat{\mathrm{j}}-\hat{\mathrm{k}})$

$\overline{\mathrm{r}}=(\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+3 \hat{\mathrm{k}})+\lambda(\hat{\mathrm{i}}-\hat{\mathrm{j}}+\hat{\mathrm{k}})$

MHT CET 2024 2nd May Evening Shift

MCQ (Single Correct Answer)

-0

Let $P$ be the image of the point $(3,1,7)$ with respect to the plane $x-y+z=3$. Then the equation of the plane passing through $P$ and containing the straight line $\frac{x}{1}=\frac{y}{2}=\frac{z}{1}$ is

$-4 y-x+7 z=0$

$x-4 y-7 z=0$

$x-4 y+7 z=0$

$x+4 y+7 z=0$

MHT CET 2024 2nd May Evening Shift

MCQ (Single Correct Answer)

-0

The incentre of the triangle whose vertices are $P(0,3,0), Q(0,0,4)$ and $R(0,3,4)$ is

$(0,3,2)$

$(0,2,3)$

$(2,0,3)$

$(2,3,0)$

MHT CET 2024 2nd May Morning Shift

MCQ (Single Correct Answer)

-0

The vector equation of a line whose Cartesian equations are $y=2,4 x-3 z+5=0$ is

$\overline{\mathrm{r}}=(3 \hat{\mathrm{i}}+4 \mathrm{k})+\lambda\left(2 \hat{\mathrm{j}}+\frac{5}{3} \hat{\mathrm{k}}\right)$

$\overline{\mathrm{r}}=(3 \hat{\mathrm{i}}+4 \mathrm{k})+\lambda\left(2 \hat{\mathrm{j}}-\frac{5}{3} \hat{\mathrm{k}}\right)$

$\overline{\mathrm{r}}=\left(2 \hat{\mathrm{j}}+\frac{5}{3} \hat{\mathrm{k}}\right)+\lambda(3 \hat{\mathrm{i}}+4 \mathrm{k})$

$\overline{\mathrm{r}}=\left(2 \hat{\mathrm{j}}-\frac{5}{3} \hat{\mathrm{k}}\right)+\lambda(3 \hat{\mathrm{i}}+4 \mathrm{k})$

PREVIOUS NEXT

MHT CET Subjects