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

The vectors $\overline{\mathrm{a}}$ and $\overline{\mathrm{b}}$ are not perpendicular and $\overline{\mathrm{c}}$ and $\overline{\mathrm{d}}$ are two vectors satisfying $\overline{\mathrm{b}} \times \overline{\mathrm{c}}=\overline{\mathrm{b}} \times \overline{\mathrm{d}}$ and $\overline{\mathrm{a}} \cdot \overline{\mathrm{d}}=0$, then the vector $\overline{\mathrm{d}}$ is equal to

A
$\overline{\mathrm{b}}+\left(\frac{\overline{\mathrm{b}} \cdot \overline{\mathrm{c}}}{\overline{\mathrm{a}} \cdot \overline{\mathrm{b}}}\right) \overline{\mathrm{c}}$
B
$\overline{\mathrm{c}}-\left(\frac{\overline{\mathrm{a}} \cdot \overline{\mathrm{c}}}{\overline{\mathrm{a}} \cdot \overline{\mathrm{b}}}\right) \overline{\mathrm{b}}$
C
$\bar{b}-\left(\frac{\bar{b} \cdot \bar{c}}{\bar{a} \cdot \bar{b}}\right) \bar{c}$
D
$\overline{\mathrm{c}}+\left(\frac{\overline{\mathrm{a}} \cdot \overline{\mathrm{c}}}{\overline{\mathrm{a}} \cdot \overline{\mathrm{b}}}\right) \overline{\mathrm{b}}$
2
MHT CET 2024 3rd May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $\overline{\mathrm{a}}=\frac{1}{\sqrt{10}}(4 \hat{\mathrm{i}}-3 \hat{\mathrm{j}}+\hat{\mathrm{k}}), \overline{\mathrm{b}}=\frac{1}{5}(\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+2 \hat{\mathrm{k}})$, then the value of $(2 \bar{a}-\bar{b}) \cdot\{(\bar{a} \times \bar{b}) \times(\bar{a}+2 \bar{b})\}$ is

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

If $\bar{a}=a_1 \hat{i}+a_2 \hat{j}+a_3 \hat{k}, \bar{b}=b_1 \hat{i}+b_2 \hat{j}+b_3 \hat{k} \quad$ and $\bar{c}=c_1 \hat{i}+c_2 \hat{j}+c_3 \hat{k}$ are non-zero non-coplanar vectors and $m$ is non-zero scalar such that $[\mathrm{m} \overline{\mathrm{a}}+\overline{\mathrm{b}} \quad \mathrm{m} \overline{\mathrm{b}}+\overline{\mathrm{c}} \mathrm{m} \overline{\mathrm{c}}+\overline{\mathrm{a}}]=28[\overline{\mathrm{a}} \overline{\mathrm{b}} \overline{\mathrm{c}}]$, then the value of $m$ is equal to

A
2
B
3
C
4
D
7
4
MHT CET 2024 3rd May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If the vectors $\overline{A B}=3 \hat{i}+4 \hat{k}$ and $\overline{A C}=5 \hat{i}-2 \hat{j}+4 \hat{k}$ are the sides of the triangle $A B C$, then the length of the median through $A$ is

A
$\sqrt{45}$ units
B
$\sqrt{18}$ units
C
$\sqrt{72}$ units
D
$\sqrt{33}$ units
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