1
MHT CET 2021 24th September Evening Shift
+2
-0

If $$\bar{a}=3 \hat{i}+\hat{j}-\hat{k}, \bar{b}=2 \hat{i}-\hat{j}+23 \hat{k}$$ and $$\bar{c}=7 \hat{i}-\hat{j}+23 \hat{k}$$, then which of the following is valid.

A
$$\bar{a}, \bar{b}, \bar{c}$$ are mutually perpendicular.
B
$$\bar{a}, \bar{b}, \bar{c}$$ are non-coplanar.
C
$$\bar{a}$$ and $$\bar{b}$$ are collinear.
D
$$\overline{\mathrm{a}}, \overline{\mathrm{b}}, \overline{\mathrm{c}}$$ are coplanar.
2
MHT CET 2021 24th September Evening Shift
+2
-0

If the angle between the vectors $$\overline{\mathrm{a}}=2 \lambda^2 \hat{\mathrm{i}}+4 \lambda \hat{\mathrm{j}}+\hat{\mathrm{k}}$$ and $$\overline{\mathrm{b}}=7 \hat{\mathrm{i}}-2 \hat{\mathrm{j}}+\lambda \hat{\mathrm{k}}$$ is obtuse, then $$\lambda \in$$

A
$$\left(0, \frac{1}{2}\right]$$
B
$$\left(0, \frac{1}{2}\right)$$
C
$$\left[0, \frac{1}{2}\right]$$
D
$$\left[0, \frac{1}{2}\right]$$
3
MHT CET 2021 24th September Evening Shift
+2
-0

If $$\bar{a}+\bar{b}, \bar{b}+\bar{c}, \bar{c}+\bar{a}$$ are coterminus edges of a parallelopiped, then its volume is

A
0
B
$$4[\bar{b} \overline{\mathrm{a}} \overline{\mathrm{c}}]$$
C
$$3[\bar{a} \bar{c} \bar{b}]$$
D
$$2[\bar{a} \bar{b} \bar{c}]$$
4
MHT CET 2021 24th September Morning Shift
+2
-0

$$\vec{a}=4 \hat{i}+13 \hat{j}-18 \hat{k}, \vec{b}=\hat{i}-2 \hat{j}+3 \hat{k}$$ and $$\vec{c}=2 \hat{i}+3 \hat{j}-4 \hat{k}$$ are three vectors such that $$\vec{a}=x \vec{b}+y \vec{c}$$, then $$x+y=$$

A
$$-1$$
B
$$-2$$
C
5
D
1
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