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

The position vector of the point of inersection of the medians of a triangle, whose vertices are $$A(1,2,3), B(1,0,3)$$ and $$C(4,1,-3)$$ is

A
$$6 \hat{i}+3 \hat{j}+3 \hat{k}$$
B
$$2 \hat{i}+\hat{j}+\hat{k}$$
C
$$3 \hat{i}+\hat{j}+\hat{k}$$
D
$$\hat{i}+\hat{j}+\hat{k}$$
2
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
3
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
$$\pi^{\mathrm{c}}$$
4
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
$$2(\hat{i}-\hat{j} \pm \sqrt{2} \hat{k})$$
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