MHT CET 2026 20th April Morning Shift | Vector Algebra Question 9 | Mathematics

If $\bar{a}$ and $\bar{b}$ are unit vectors perpendicular to each other, then $\left[\bar{a} + (\bar{a} \times \bar{b})\quad \bar{b} + (\bar{a} \times \bar{b})\quad (\bar{a} \times \bar{b})\right] = \cdots$

$-1$

$1$

$2$

$3$

MHT CET 2026 20th April Morning Shift

MCQ (Single Correct Answer)

-0

If $\bar{a}$, $\bar{b}$ and $\bar{c}$ are three vectors such that $|\bar{a} + \bar{b} + \bar{c}| = 1$, $\bar{c} = \lambda(\bar{a} \times \bar{b})$ and $|\bar{a}| = \dfrac{1}{\sqrt{3}}$, $|\bar{b}| = \dfrac{1}{\sqrt{2}}$, $|\bar{c}| = \dfrac{1}{\sqrt{6}}$, then the angle between $\bar{a}$ and $\bar{b}$ is

$\dfrac{\pi^c}{6}$

$\dfrac{\pi^c}{4}$

$\dfrac{\pi^c}{3}$

$\dfrac{\pi^c}{2}$

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

$\frac{1}{2}$

$\frac{5}{2}$

$\frac{3}{2}$

MHT CET 2025 5th May Evening Shift

MCQ (Single Correct Answer)

-0

If $\overline{\mathrm{c}}=5 \overline{\mathrm{a}}+6 \overline{\mathrm{~b}}$ and $3 \overline{\mathrm{c}}=\overline{\mathrm{a}}-4 \overline{\mathrm{~b}}$ then

$\bar{a}, \bar{b}, \bar{c}$ are non-collinear

$\overline{\mathrm{a}}, \overline{\mathrm{b}}, \overline{\mathrm{c}}$ are in the same direction

$\overline{\mathrm{a}}, \overline{\mathrm{c}}$ are in the same direction but $\overline{\mathrm{a}}, \overline{\mathrm{b}}$ are in the opposite direction

$\overline{\mathrm{c}}, \overline{\mathrm{b}}$ are in the opposite direction and $\overline{\mathrm{a}}, \overline{\mathrm{b}}$ are in the same direction

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