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

If the points $\mathrm{P}, \mathrm{Q}$ and R are with the position vectors $\hat{i}-2 \hat{j}+3 \hat{k},-2 \hat{i}+3 \hat{j}+2 \hat{k}$ and $-8 \hat{i}+13 \hat{j}$ respectively, then these points are

A
collinear and $Q$ lies between $P$ and $R$.
B
collinear and $R$ lies between $P$ and $Q$.
C
collinear and $P$ lies between $Q$ and $R$.
D
non-collinear.
2
MHT CET 2024 15th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

One side and one diagonal of a parallelogram are represented by $3 \hat{i}+\hat{j}-\hat{k}$ and $2 \hat{i}+\hat{j}-2 \hat{k}$ respectively, then the area of parallelogram in square units is

A
$2 \sqrt{3}$
B
$3 \sqrt{2}$
C
$6 \sqrt{2}$
D
$4 \sqrt{3}$
3
MHT CET 2024 15th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If the vector $\overline{\mathrm{c}}$ lies in the plane of $\overline{\mathrm{a}}$ and $\overline{\mathrm{b}}$, where $\overline{\mathrm{a}}=\hat{\mathrm{i}}-\hat{\mathrm{j}}+2 \hat{\mathrm{k}}, \overline{\mathrm{b}}=\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}}$ and $\overline{\mathrm{c}}=x \hat{\mathrm{i}}-(2-x) \hat{\mathrm{j}}-\hat{\mathrm{k}}$, then the value of $x$ is

A
4
B
$-$4
C
2
D
$-$2
4
MHT CET 2024 15th May Morning Shift
MCQ (Single Correct Answer)
+2
-0

Let $\overline{\mathrm{a}}=\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}}, \overline{\mathrm{b}}=\hat{\mathrm{i}}-\hat{\mathrm{j}}+\hat{\mathrm{k}}$ and $\overline{\mathrm{c}}=\hat{\mathrm{i}}-\hat{\mathrm{j}}-\hat{\mathrm{k}}$ be three vectors. A vector $\bar{v}$ in the plane of $\overline{\mathrm{a}}$ and $\overline{\mathrm{b}}$, whose projection on $\overline{\mathrm{c}}$ is $\frac{1}{\sqrt{3}}$, is given by

A
$\hat{i}-3 \hat{j}+3 \hat{k}$
B
$-3 \hat{i}-3 \hat{j}-\hat{k}$
C
$3 \hat{i}-\hat{j}+3 \hat{k}$
D
$\hat{\mathrm{i}}+3 \hat{\mathrm{j}}-3 \hat{\mathrm{k}}$
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