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

$$\overline{\mathrm{a}}, \overline{\mathrm{b}}$$ and $$\overline{\mathrm{c}}$$ are three vectors such that $$\overline{\mathrm{a}}+\overline{\mathrm{b}}+\overline{\mathrm{c}}=\overline{0}$$ and $$|\overline{\mathrm{a}}|=3,|\overline{\mathrm{b}}|=5,|\overline{\mathrm{c}}|=7$$, then the angle between $$\overline{\mathrm{a}}$$ and $$\bar{b}$$ is

A
$$\frac{\pi}{4}$$
B
$$\frac{\pi}{2}$$
C
$$\frac{\pi}{3}$$
D
$$\frac{\pi}{6}$$
2
MHT CET 2021 20th September Evening Shift
+2
-0

If area of the parallelogram with $$\bar{a}$$ and $$\bar{b}$$ as two adjacent sides is 20 square units, then the area of the parallelogram having $$3 \overline{\mathrm{a}}+\overline{\mathrm{b}}$$ and $$2 \overline{\mathrm{a}}+3 \overline{\mathrm{b}}$$ as two adjacent sides in square units is

A
105
B
120
C
75
D
140
3
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
$$\overline{\mathrm{r}}=\frac{1}{3} \overline{\mathrm{a}}-\frac{1}{3} \overline{\mathrm{b}}$$
4
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
MHT CET Subjects
Physics
Mechanics
Optics
Electromagnetism
Modern Physics
Chemistry
Physical Chemistry
Inorganic Chemistry
Organic Chemistry
Mathematics
Algebra
Trigonometry
Calculus
Coordinate Geometry
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