1
MHT CET 2024 9th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $\overline{\mathrm{a}}=\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}}, \overline{\mathrm{a}} \cdot \overline{\mathrm{b}}=1$ and $\overline{\mathrm{a}} \times \overline{\mathrm{b}}=\hat{\mathrm{j}}-\hat{\mathrm{k}}$, then $\overline{\mathrm{b}}$ is

A
$\hat{i}-\hat{j}+\hat{k}$
B
$2 \hat{j}-\hat{k}$
C
$\hat{i}$
D
$2 \hat{\mathrm{i}}$
2
MHT CET 2024 9th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If the area of the parallelogram with $\bar{a}$ and $\bar{b}$ as two adjacent sides is 15 square units, then the area (in square units) of the parallelogram, having $3 \bar{a}+2 \bar{b}$ and $\bar{a}+3 \bar{b}$ as two adjacent sides, is

A
45
B
75
C
105
D
120
3
MHT CET 2024 4th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

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

A
$\frac{\pi}{6}$
B
$\frac{\pi}{3}$
C
$\frac{\pi}{4}$
D
$\frac{\pi}{2}$
4
MHT CET 2024 4th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $\bar{a}, \bar{b}, \bar{c}$ are non-coplanar vectors and $\overline{\mathrm{p}}=\frac{\overline{\mathrm{b}} \times \overline{\mathrm{c}}}{[\overline{\mathrm{a}} \overline{\mathrm{b}} \overline{\mathrm{c}}]}, \overline{\mathrm{q}}=\frac{\overline{\mathrm{c}} \times \overline{\mathrm{a}}}{[\overline{\mathrm{a}} \overline{\mathrm{b}} \overline{\mathrm{c}}]}, \overline{\mathrm{r}}=\frac{\overline{\mathrm{a}} \times \overline{\mathrm{b}}}{[\overline{\mathrm{a}} \overline{\mathrm{b}} \overline{\mathrm{c}}]}$, then $2 \overline{\mathrm{a}} \cdot \overline{\mathrm{p}}+\overline{\mathrm{b}} \cdot \overline{\mathrm{q}}+\overline{\mathrm{c}} \cdot \overline{\mathrm{r}}=$

A
0
B
3
C
4
D
1
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