MHT CET 2025 19th April Morning Shift | Vector Algebra Question 26 | Mathematics

If $\left[\begin{array}{lll}2 \bar{p}-3 \bar{r} & \bar{q} & \bar{s}\end{array}\right]+\left[\begin{array}{lll}3 \bar{p}+2 \bar{q} & \bar{r} & \bar{s}\end{array}\right]=m\left[\begin{array}{lll}\bar{p} & \bar{r} & \bar{s}\end{array}\right] +n\left[\begin{array}{lll}\bar{q} & \bar{r} & \bar{s}\end{array}\right]+t\left[\begin{array}{lll}\bar{p} & \bar{q} & \bar{s}\end{array}\right]$, then the values of $\mathrm{m}, \mathrm{n}, \mathrm{t}$ respectively are ....

$2,3,3$

$3,4,5$

$1,2,3$

$3,5,2$

MHT CET 2025 19th April Morning Shift

MCQ (Single Correct Answer)

-0

The volume of the tetrahedron whose co-terminus edges are $\bar{a}, \bar{b}, \bar{c}$ is 12 cubic units. If the scalar projection of $\bar{a}$ on $\bar{b} \times \bar{c}$ is 4 , then $|\overline{\mathrm{b}} \times \overline{\mathrm{c}}|=$

$18$

$\frac{1}{18}$

$16$

$\frac{1}{16}$

MHT CET 2024 16th May Evening Shift

MCQ (Single Correct Answer)

-0

If $\overline{\mathrm{a}}=\hat{\mathrm{i}}-2 \hat{\mathrm{j}}+3 \hat{\mathrm{k}}$ and $\overline{\mathrm{b}}=2 \hat{i}+3 \hat{\mathrm{j}}-\hat{\mathrm{k}}$ are two vectors, then the angle between the vectors $3 \overline{\mathrm{a}}+5 \overline{\mathrm{~b}}$ and $5 \overline{\mathrm{a}}+3 \overline{\mathrm{~b}}$ is

$\cos ^{-1}\left(\frac{10}{19}\right)$

$\cos ^{-1}\left(\frac{11}{19}\right)$

$\cos ^{-1}\left(\frac{13}{19}\right)$

$\cos ^{-1}\left(\frac{14}{19}\right)$

MHT CET 2024 16th May Evening Shift

MCQ (Single Correct Answer)

-0

If $\overline{\mathrm{a}}$ is perpendicular to $\bar{b}$ and $\bar{c},|\bar{a}|=2$, $|\overline{\mathrm{b}}|=3,|\overline{\mathrm{c}}|=4$ and the angle between $\overline{\mathrm{b}}$ and $\overline{\mathrm{c}}$ is $\frac{\pi}{3}$, then $\left[\begin{array}{lll}\overline{\mathrm{a}} & \overline{\mathrm{b}} & \overline{\mathrm{c}}\end{array}\right]=$

$4 \sqrt{3}$

$6 \sqrt{3}$

$24 \sqrt{3}$

$12 \sqrt{3}$

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