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

Let $\overline{\mathrm{u}}=\hat{\mathrm{i}}+\hat{\mathrm{j}}, \overline{\mathrm{v}}=\hat{\mathrm{i}}-\hat{\mathrm{j}}$ and $\overline{\mathrm{w}}=\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+3 \hat{\mathrm{k}}$. If $\hat{\mathrm{n}}$ is a unit vector such that $\overline{\mathbf{u}} \cdot \hat{\mathrm{n}}=0$ and $\overline{\mathrm{v}} \cdot \hat{\mathrm{n}}=0$, then $|\overline{\mathrm{w}} \cdot \hat{\mathrm{n}}|$ is equal to

A
0
B
1
C
2
D
3
2
MHT CET 2024 11th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

Let $\bar{a}, \bar{b}$ and $\bar{c}$ be three unit vectors such that $\overline{\mathrm{a}} \times(\overline{\mathrm{b}} \times \overline{\mathrm{c}})=\frac{\sqrt{3}}{2}(\overline{\mathrm{~b}}+\overline{\mathrm{c}})$. If $\bar{b}$ is not parallel to $\bar{c}$, then the angle between $\bar{a}$ and $\bar{b}$ is

A
$\frac{3 \pi}{4}$
B
$\frac{\pi}{2}$
C
$\frac{2 \pi}{3}$
D
$\frac{5 \pi}{6}$
3
MHT CET 2024 11th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $\hat{a}=\frac{1}{\sqrt{10}}(3 \hat{i}+\hat{k})$ and $\hat{b}=\frac{1}{7}(2 \hat{i}+3 \hat{j}-6 \hat{k})$, then the value of $(2 \hat{a}-\hat{b}) \cdot[(\hat{a} \times \hat{b}) \times(\hat{a}+2 \hat{b})]$ is

A
5
B
3
C
$-$5
D
$-$3
4
MHT CET 2024 11th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

Let $\overline{\mathrm{a}}, \overline{\mathrm{b}}$, and $\overline{\mathrm{c}}$ be three non-zero vectors such that no two of these are collinear. If the vector $\bar{a}+2 \bar{b}$ is collinear with $\bar{c}$ and $\bar{b}+3 \bar{c}$ is collinear with $\overline{\mathrm{a}}$, then $\overline{\mathrm{a}}+2 \overline{\mathrm{~b}}+6 \overline{\mathrm{c}}$ equals

A
$\lambda \bar{c}(\lambda$ being some non-zero scalar)
B
$\overline{\mathrm{b}}(\lambda$ being some non-zero scalar)
C
$\lambda \overline{\mathrm{a}}$ ( $\lambda$ being some non-zero scalar)
D
$\overline{0}$ ( $\lambda$ being some non-zero scalar)
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