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

$$(2 \hat{\mathrm{i}}+6 \hat{\mathrm{i}}+27 \hat{\mathrm{k}}) \times(\hat{\mathrm{i}}+\lambda \hat{\mathrm{j}}+\mu \hat{\mathrm{k}})=\overline{0}$$, then $$\lambda$$ and $$\mu$$ are respectively

A
$$\frac{17}{2}, 3$$
B
$$3, \frac{17}{2}$$
C
$$3, \frac{27}{2}$$
D
$$\frac{27}{2}, 3$$
2
MHT CET 2020 16th October Evening Shift
+2
-0

Let $$G$$ be the centroid of a $$\triangle A B C$$ and $$\mathrm{O}_{b_\theta}$$ other point in that plane, then $$\mathrm{OA}+\mathrm{OB}+\mathrm{OC}+\mathrm{CG}=$$

A
O
B
4 OG
C
3 OG
D
2 OG
3
MHT CET 2020 16th October Evening Shift
+2
-0

If the volume of the parallelopiped whose conterminus edges are along the vectors $$\mathbf{a}, \mathbf{b}, \mathbf{c}$$ is 12, then the volume of the tetrahedron whose conterminus edges are $$\mathbf{a}+\mathbf{b}, \mathbf{b}+\mathbf{c}$$ and $$c+a$$ is

A
12 (units)$${ }^3$$
B
24 (units)$${ }^3$$
C
4 (units)$$^3$$
D
6 (units)$${ }^3$$
4
MHT CET 2020 16th October Evening Shift
+2
-0

For any non-zero vectors $$\mathbf{a}$$ and $$\mathbf{b}$$,

A
$$a \times b$$
B
$$|a \times b|^2$$
C
0
D
$$|\mathbf{a} \times \mathbf{b}|$$
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