1
MHT CET 2021 22th September Morning Shift
+2
-0

The area of the parallelogram whose diagonals are represented by the vectors $$\bar{a}=3 \hat{i}-\hat{j}-2 \hat{k}$$ and $$\bar{b}=-\hat{i}+3 \hat{j}-3 \hat{k}$$ is

A
$$\sqrt{266}$$ sq. units
B
$$\frac{1}{2} \sqrt{266}$$ sq. units
C
266 sq. units
D
122 sq. units
2
MHT CET 2021 22th September Morning Shift
+2
-0

If $$\overline{\mathrm{a}}+\overline{\mathrm{b}}+\overline{\mathrm{c}}=\overline{0}$$ with $$|\overline{\mathrm{a}}|=3,|\overline{\mathrm{b}}|=5$$ and $$|\overline{\mathrm{c}}|=7$$, then angle between $$\overline{\mathrm{a}}$$ and $$\overline{\mathrm{b}}$$ is

A
$$\left(\frac{\pi}{3}\right)^{\mathrm{c}}$$
B
$$\left(\frac{4 \pi}{3}\right)^c$$
C
$$\left(\frac{2 \pi}{3}\right)^{\mathrm{c}}$$
D
$$\pi^{\mathrm{c}}$$
3
MHT CET 2021 22th September Morning Shift
+2
-0

If $$|\bar{u}|=2$$ and $$\bar{u}$$ makes angles of $$60^{\circ}$$ and $$120^{\circ}$$ with axes $$\mathrm{OX}$$ and $$\mathrm{OY}$$ in the origin, then $$\bar{u}=$$

A
$$\hat{i}+\hat{j}+\sqrt{2} \hat{k}$$
B
$$2(\hat{i}+\hat{j} \pm \sqrt{2} \hat{k})$$
C
$$2(\hat{i}-\hat{j}+\sqrt{2} \hat{k})$$
D
$$2(\hat{i}-\hat{j} \pm \sqrt{2} \hat{k})$$
4
MHT CET 2021 22th September Morning Shift
+2
-0

If $$\overline{\mathrm{a}}, \overline{\mathrm{b}}, \overline{\mathrm{c}}$$ are mutually perpendicular vectors having magnitudes $$1,2,3$$ respectively, then $$\left[\begin{array}{lll}\overline{\mathrm{a}}+\overline{\mathrm{b}}+\overline{\mathrm{c}} & \overline{\mathrm{b}}-\overline{\mathrm{a}} & \overline{\mathrm{c}}\end{array}\right]=$$

A
12
B
18
C
0
D
6
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