1
MHT CET 2024 3rd May Evening Shift
MCQ (Single Correct Answer)
+2
-0

Let $\overline{\mathrm{a}}=\hat{\mathrm{j}}-\hat{\mathrm{k}}$ and $\overline{\mathrm{c}}=\hat{\mathrm{i}}-\hat{\mathrm{j}}-\hat{\mathrm{k}}$. Then the vector $\overline{\mathrm{b}}$ satisfying $\overline{\mathrm{a}} \times \overline{\mathrm{b}}+\overline{\mathrm{c}}=\overline{0}$ and $\overline{\mathrm{a}} \cdot \overline{\mathrm{b}}=3$, is

A
$-\hat{i}+\hat{j}-2 \hat{k}$
B
$2 \hat{i}-\hat{j}+2 \hat{k}$
C
$\hat{i}-\hat{j}-2 \hat{k}$
D
$\hat{i}+\hat{j}-2 \hat{k}$
2
MHT CET 2024 3rd May Morning Shift
MCQ (Single Correct Answer)
+2
-0

The area (in sq. units) of the parallelogram whose diagonals are along the vectors $8 \hat{\mathrm{i}}-6 \hat{\mathrm{j}}$ and $3 \hat{i}+4 \hat{j}-12 \hat{k}$, is

A
52
B
26
C
65
D
20
3
MHT CET 2024 3rd May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $|\bar{a}|=\sqrt{27},|\bar{b}|=7$ and $|\bar{a} \times \bar{b}|=35$, then $\bar{a} \cdot \bar{b}$ is equal to

A
$\sqrt{\frac{35}{2}}$
B
$\frac{\sqrt{35}}{2}$
C
$7 \sqrt{2}$
D
$\sqrt{35}$
4
MHT CET 2024 3rd May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $\mathrm{A} \equiv(1,-1,0), \mathrm{B} \equiv(0,1,-1)$ and $\mathrm{C} \equiv(-1,0,1)$, then the unit vector $\overline{\mathrm{d}}$ such that $\overline{\mathrm{a}}$ and $\overline{\mathrm{d}}$ are perpendiculars and $\overline{\mathrm{b}}, \overline{\mathrm{c}}, \overline{\mathrm{d}}$ are coplanar is

A
$+\frac{1}{\sqrt{3}}(1,1,1)$
B
$+\frac{1}{\sqrt{3}}(-1,-1,1)$
C
$+\frac{1}{\sqrt{6}}(1,1,-2)$
D
$+\frac{1}{\sqrt{2}}(1,1,0)$
MHT CET Subjects
EXAM MAP