1
MHT CET 2025 19th April Evening Shift
MCQ (Single Correct Answer)
+2
-0

The projection of the line segment joining the points $(2,1,-3)$ and $(-1,0,2)$ on the line whose direction ratios are $3,2,6$ is

A
$\frac{19}{7}$ units
B
$\frac{17}{7}$ units
C
$\frac{11}{7}$ units
D
$\frac{15}{7}$ units
2
MHT CET 2025 19th April Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $\bar{a}, \bar{b}, \bar{c}$ are three vectors such that $|\bar{a}|=3$, $|\bar{b}|=5,|\bar{c}|=7$ then $|\bar{a}-\bar{b}|^2+|\bar{b}-\bar{c}|^2+|\bar{c}-\bar{a}|^2$ does not exceed

A
83
B
249
C
166
D
105
3
MHT CET 2025 19th April Morning Shift
MCQ (Single Correct Answer)
+2
-0
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 ....
A
$2,3,3$
B
$3,4,5$
C
$1,2,3$
D
$3,5,2$
4
MHT CET 2025 19th April Morning Shift
MCQ (Single Correct Answer)
+2
-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 $|\overline{\mathrm{b}} \times \overline{\mathrm{c}}|=$
A
$18$
B
$\frac{1}{18}$
C
$16$
D
$\frac{1}{16}$
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