1
MHT CET 2021 20th September Evening Shift
+2
-0

If $$\bar{r}=-4 \hat{i}-6 \hat{j}-2 \hat{k}$$ is a linear combination of the vectors $$\bar{a}=-\hat{i}+4 \hat{j}+3 \hat{k}$$ and $$\bar{b}=-8 \hat{i}-\hat{j}+3 \hat{k}$$, then

A
$$\overline{\mathrm{r}}=\frac{-4}{3} \overline{\mathrm{a}}+\frac{2}{3} \overline{\mathrm{b}}$$
B
$$\overline{\mathrm{r}}=\frac{4}{3} \overline{\mathrm{a}}+\frac{2}{3} \bar{b}$$
C
$$\overline{\mathrm{r}}=\frac{-1}{3} \overline{\mathrm{a}}+\frac{2}{3} \overline{\mathrm{b}}$$
D
$$\overline{\mathrm{r}}=\frac{1}{3} \overline{\mathrm{a}}-\frac{1}{3} \overline{\mathrm{b}}$$
2
MHT CET 2021 20th September Morning Shift
+2
-0

If the volume of a tetrahedron whose conterminous edges are $$\vec{\mathrm{a}}+\vec{\mathrm{b}}, \vec{\mathrm{b}}+\vec{\mathrm{c}}, \vec{\mathrm{c}}+\vec{\mathrm{a}}$$ is 24 cubic units, then the volume of parallelopiped whose coterminous edges are $$\vec{\mathrm{a}}, \vec{\mathrm{b}}, \vec{\mathrm{c}}$$ is

A
48 cubic units
B
144 cubic units
C
72 cubic units
D
10 cubic units
3
MHT CET 2021 20th September Morning Shift
+2
-0

If $$\overline{\mathrm{e}}_1, \overline{\mathrm{e}}_2$$ and $$\overline{\mathrm{e}}_1+\overline{\mathrm{e}}_2$$ are unit vectors, then the angle between $$\overline{\mathrm{e}}_1$$ and $$\overline{\mathrm{e}}_2$$ is

A
$$150^{\circ}$$
B
$$120^{\circ}$$
C
$$90^{\circ}$$
D
$$135^{\circ}$$
4
MHT CET 2021 20th September Morning Shift
+2
-0

If $$\overline{\mathrm{a}}, \overline{\mathrm{b}} , \overline{\mathrm{c}}$$ are three vectors which are perpendicular to $$\overline{\mathrm{b}}+\overline{\mathrm{c}}, \overline{\mathrm{c}}+\overline{\mathrm{a}}$$ and $$\overline{\mathrm{a}}+\overline{\mathrm{b}}$$ respectively, such that $$|\bar{a}|=2,|\bar{b}|=3,|\bar{c}|=4$$, then $$|\bar{a}+\bar{b}+\bar{c}|=$$

A
29
B
3
C
9
D
$$\sqrt{29}$$
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