MHT CET 2026 15th April Morning Shift | Vector Algebra Question 52 | Mathematics

The vector $\bar{r}$ whose magnitude is $3\sqrt{2}$ units and which makes angles of $\dfrac{\pi}{4}$ and $\dfrac{\pi}{2}$ with the positive y- and z-axes respectively is....

$\hat{i} \pm 3\hat{j}$

$\hat{i} \pm \hat{j}$

$-\hat{i} \pm \hat{j}$

$\pm 3\hat{i} + 3\hat{j}$

MHT CET 2026 15th April Morning Shift

MCQ (Single Correct Answer)

-0

Let $(\bar{p} \wedge \bar{q})$ denote the angle between $\bar{p}$ and $\bar{q}$. If $\bar{a} + \bar{b} + \bar{c} = \bar{0}, |\bar{a}| = 7, |\bar{b}| = 5$ and $|\bar{c}| = 3$ then (take $\pi = \dfrac{22}{7}$)

$\sin(\bar{b} \wedge \bar{c}) = \dfrac{1}{2}$

$\cos(\bar{a} \wedge \bar{c}) = -\dfrac{\pi}{4}$

$\cos(\bar{b} \wedge \bar{c}) = -\dfrac{1}{2}$

$\sin(\bar{a} \wedge \bar{c}) = \dfrac{\pi}{4}$

MHT CET 2026 15th April Morning Shift

MCQ (Single Correct Answer)

-0

If a unit vector makes angles $\dfrac{\pi}{4}$ with $\hat{i}$, $\dfrac{\pi}{3}$ with $\hat{j}$ and $\theta \in (0, \pi)$ with $\hat{k}$, then a value of $\theta$ is equal to...

$\dfrac{\pi}{3}, \dfrac{2\pi}{3}$

$\dfrac{\pi}{6}, \dfrac{5\pi}{6}$

$\dfrac{\pi}{4}, \dfrac{5\pi}{4}$

$\dfrac{5\pi}{12}, \dfrac{7\pi}{12}$

MHT CET 2025 5th May Evening Shift

MCQ (Single Correct Answer)

-0

ABCD is a quadrilateral with $\overline{\mathrm{AB}}=\overline{\mathrm{a}}, \overline{\mathrm{AD}}=\overline{\mathrm{b}}$ and $\overline{\mathrm{AC}}=2 \overline{\mathrm{a}}+3 \overline{\mathrm{~b}}$. If its area is $\alpha$ times the area of the parallelogram with $\mathrm{AB}, \mathrm{AD}$ as adjacent sides, then the value of $\alpha$ is

$\frac{1}{2}$

$\frac{5}{2}$

$\frac{3}{2}$

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