1
MHT CET 2024 15th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If the points $\mathrm{P}, \mathrm{Q}$ and R are with the position vectors $\hat{i}-2 \hat{j}+3 \hat{k},-2 \hat{i}+3 \hat{j}+2 \hat{k}$ and $-8 \hat{i}+13 \hat{j}$ respectively, then these points are

A
collinear and $Q$ lies between $P$ and $R$.
B
collinear and $R$ lies between $P$ and $Q$.
C
collinear and $P$ lies between $Q$ and $R$.
D
non-collinear.
2
MHT CET 2024 15th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

A line makes $45^{\circ}$ angle with positive X -axis and makes equal angles with positive Y -axis ad Z-axis respectively, then the sum of the three angles which the line makes with positive X -axis, Y -axis and Z -axis is

A
$135^{\circ}$
B
$150^{\circ}$
C
$165^{\circ}$
D
$180^{\circ}$
3
MHT CET 2024 15th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If the lines $\frac{x-1}{2}=\frac{y+2}{3}=\frac{z-1}{4}$ and $\frac{x-3}{1}=\frac{y-\mathrm{k}}{2}=\frac{\mathrm{z}}{1}$ intersect, then k has the value

A
$\frac{7}{2}$
B
$\frac{3}{2}$
C
$\frac{-7}{2}$
D
$\frac{-3}{2}$
4
MHT CET 2024 15th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The vector equation of the plane through the line of intersection of the planes $x+y+z=1$ and $2 x+3 y+4 z=5$, which is perpendicular to the plane $x-y+z=0$, is

A
$\overline{\mathrm{r}} \cdot(\hat{\mathrm{i}}-\hat{\mathrm{k}})=2$
B
$\overline{\mathrm{r}} \cdot(\hat{\mathrm{i}}+\hat{\mathrm{k}})+2=0$
C
$\overline{\mathrm{r}} \cdot(\hat{\mathrm{i}}+\hat{\mathrm{k}})=2$
D
$\overline{\mathrm{r}} \cdot(\hat{\mathrm{i}}-\hat{\mathrm{k}})+2=0$
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