MHT CET 2026 17th April Morning Shift | Three Dimensional Geometry Question 35 | Mathematics

The equation of a line in cartesian form passing through (0, 0, 0) and (4, 3, c) and parallel to $\vec{a} \times \vec{b}$ where $\vec{a} = 2\hat{i} + \hat{j} + 2\hat{k}$, $\vec{b} = 3\hat{i} - 4\hat{j}$ is

$\dfrac{x-4}{8} = \dfrac{y-3}{6} = \dfrac{z + \frac{11}{2}}{11}$

$\dfrac{x-4}{8} = \dfrac{y+3}{6} = \dfrac{z + \frac{11}{2}}{-11}$

$\dfrac{x-4}{8} = \dfrac{y-3}{6} = \dfrac{z + \frac{11}{2}}{-11}$

$\dfrac{x+4}{8} = \dfrac{y-3}{6} = \dfrac{z + \frac{11}{2}}{-11}$

MHT CET 2026 16th April Evening Shift

MCQ (Single Correct Answer)

-0

If the lines $2x = ky = -z$ and $6x = -y = -4z$ are perpendicular to each other then the value of $k$ is ...

$16$

$5$

$10$

$3$

MHT CET 2026 16th April Evening Shift

MCQ (Single Correct Answer)

-0

The vector equation of plane in parametric form, passing through the points (-1, 2, 0), (2, 2, -1) and parallel to the line $\dfrac{x-1}{1} = \dfrac{2y+1}{2} = \dfrac{z+1}{-1}$ is

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

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

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

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

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