1
MHT CET 2024 16th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $\bar{a}=2 \hat{i}-\hat{j}+\hat{k}, \bar{b}=\hat{i}+\hat{j}-2 \hat{k}$ and $\bar{c}=4 \hat{i}-2 \hat{j}+\hat{k}$, then the unit vector in the direction of $3 \overline{\mathrm{a}}+\overline{\mathrm{b}}-2 \overline{\mathrm{c}}$ is

A
$\frac{1}{\sqrt{6}}(-\hat{i}+2 \hat{j}-\hat{k})$
B
$\frac{1}{\sqrt{6}}(\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+\hat{\mathrm{k}})$
C
$\frac{1}{\sqrt{6}}(2 \hat{i}-\hat{j}-\hat{k})$
D
$\frac{1}{\sqrt{6}}(-\hat{\mathrm{i}}-2 \hat{\mathrm{j}}+\hat{\mathrm{k}})$
2
MHT CET 2024 16th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

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

A
6
B
$-$6
C
8
D
$-$8
3
MHT CET 2024 16th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $\overline{\mathrm{a}}, \overline{\mathrm{b}}, \overline{\mathrm{c}}$ are three vectors such that $\overline{\mathrm{a}} \neq \overline{0}$ and $\overline{\mathrm{a}} \times \overline{\mathrm{b}}=2 \overline{\mathrm{a}} \times \overline{\mathrm{c}},|\overline{\mathrm{a}}|=|\overline{\mathrm{c}}|=1,|\overline{\mathrm{~b}}|=4$ and $|\overline{\mathrm{b}} \times \overline{\mathrm{c}}|=\sqrt{15}$. If $\overline{\mathrm{b}}-2 \overline{\mathrm{c}}=\lambda \overline{\mathrm{a}}$, then $\lambda$ is

A
1
B
$-$4
C
3
D
$-$2
4
MHT CET 2024 16th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $\overline{\mathrm{a}}, \overline{\mathrm{b}}$ and $\overline{\mathrm{c}}$ are unit coplanar vectors, then the scalar triple product $\left[\begin{array}{lll}2 \overline{\mathrm{a}}-\overline{\mathrm{b}} & 2 \overline{\mathrm{~b}}-\overline{\mathrm{c}} & 2 \overline{\mathrm{c}}-\overline{\mathrm{a}}\end{array}\right]$ has the value

A
0
B
1
C
$-\sqrt{3}$
D
$\sqrt{3}$
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