1
MHT CET 2024 10th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The vector of magnitude 6 units and perpendicular to vectors $2 \hat{i}+\hat{j}-3 \hat{k}$ and $\hat{\mathrm{i}}-2 \hat{\mathrm{j}}+\hat{\mathrm{k}}$ is

A
$2 \sqrt{3}(-\hat{i}+\hat{j}+\hat{k})$
B
$2 \sqrt{3}(\hat{\mathrm{i}}-\hat{\mathrm{j}}+\hat{\mathrm{k}})$
C
$2 \sqrt{3}(\hat{i}+\hat{j}+\hat{k})$
D
$2 \sqrt{3}(-\hat{\mathrm{i}}-\hat{\mathrm{j}}+\hat{\mathrm{k}})$
2
MHT CET 2024 10th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $\overline{\mathrm{a}}=\hat{\mathrm{j}}-\hat{\mathrm{k}}$ 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
$-\hat{i}+\hat{j}-\hat{k}$
C
$-\hat{i}-\hat{j}+\hat{k}$
D
$\hat{i}+\hat{j}+\hat{k}$
3
MHT CET 2024 10th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

$\overline{\mathrm{a}}=\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}}, \overline{\mathrm{b}}=4 \hat{\mathrm{i}}-2 \hat{j}+3 \hat{k}, \overline{\mathrm{c}}=\hat{i}-2 \hat{j}+\hat{k}$, then $a$ vector of magnitude 6 units, which is parallel to the vector $2 \bar{a}-\bar{b}+3 c$, is

A
$2 \hat{i}-4 \hat{j}+4 \hat{k}$
B
$\hat{i}-\hat{j}+2 \hat{k}$
C
$4 \hat{\mathrm{i}}+4 \hat{\mathrm{j}}-2 \hat{\mathrm{k}}$
D
$2 \hat{i}+4 \hat{j}+4 \hat{k}$
4
MHT CET 2024 10th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $\overline{\mathrm{a}}=2 \hat{i}+2 \hat{j}+3 \hat{k}, \bar{b}=-\hat{i}+2 \hat{j}+\hat{k}$ and $\bar{c}=3 \hat{i}+\hat{j}$ such that $\overline{\mathrm{b}}+\lambda \overline{\mathrm{a}}$ is perpendicular to $\overline{\mathrm{c}}$, then $\lambda$ is

A
  $\frac{1}{2}$
B
$\frac{1}{4}$
C
$\frac{1}{6}$
D
$\frac{1}{8}$
MHT CET Subjects
EXAM MAP