1
MHT CET 2023 9th May Evening Shift
+2
-0

Vectors $$\overline{\mathrm{a}}$$ and $$\overline{\mathrm{b}}$$ are such that $$|\overline{\mathrm{a}}|=1 ;|\overline{\mathrm{b}}|=4$$ and $$\bar{a} \cdot \bar{b}=2$$. If $$\bar{c}=2 \bar{a} \times \bar{b}-3 \bar{b}$$, then the angle between $$\bar{b}$$ and $$\bar{c}$$ is

A
$$\frac{\pi}{6}$$
B
$$\frac{5 \pi}{6}$$
C
$$\frac{\pi}{3}$$
D
$$\frac{2 \pi}{3}$$
2
MHT CET 2023 9th May Evening Shift
+2
-0

Two adjacent sides of a parallelogram are $$2 \hat{i}-4 \hat{j}+5 \hat{k}$$ and $$\hat{i}-2 \hat{j}-3 \hat{k}$$, then the unit vector parallel to its diagonal is

A
$$\frac{3}{7} \hat{\mathrm{i}}-\frac{6}{7} \hat{\mathrm{j}}+\frac{2}{7} \hat{\mathrm{k}}$$
B
$$\frac{2}{7} \hat{\mathrm{i}}-\frac{6}{7} \hat{\mathrm{j}}+\frac{3}{7} \hat{\mathrm{k}}$$
C
$$\frac{6}{7} \hat{\mathrm{i}}-\frac{2}{7} \hat{\mathrm{j}}+\frac{3}{7} \hat{\mathrm{k}}$$
D
$$\frac{1}{7} \hat{\mathrm{i}}+\frac{1}{7} \hat{\mathrm{j}}-\frac{3}{7} \hat{\mathrm{k}}$$
3
MHT CET 2023 9th May Evening Shift
+2
-0

If $$\mathrm{D}, \mathrm{E}$$ and $$\mathrm{F}$$ are the mid-points of the sides $$\mathrm{BC}$$, $$\mathrm{CA}$$ and $$\mathrm{AB}$$ of triangle $$\mathrm{ABC}$$ respectively, then $$\overline{\mathrm{AD}}+\frac{2}{3} \overline{\mathrm{BE}}+\frac{1}{3} \overline{\mathrm{CF}}=$$

A
$$\frac{1}{2} \overline{\mathrm{AB}}$$
B
$$\frac{1}{2} \overline{\mathrm{AC}}$$
C
$$\frac{1}{2} \overline{\mathrm{BC}}$$
D
$$\frac{2}{3} \overline{\mathrm{AC}}$$
4
MHT CET 2023 9th May Morning Shift
+2
-0

If two vertices of a triangle are $$\mathrm{A}(3,1,4)$$ and $$\mathrm{B}(-4,5,-3)$$ and the centroid of the triangle is $$G(-1,2,1)$$, then the third vertex $$C$$ of the triangle is

A
$$(2,0,2)$$
B
$$(-2,0,2)$$
C
$$(0,-2,2)$$
D
$$(2,-2,0)$$
EXAM MAP
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