1
MHT CET 2021 21th September Evening Shift
+2
-0

If $$\overline{\mathrm{a}}=\hat{\mathrm{i}}+2 \hat{\mathrm{j}}-3 \hat{\mathrm{k}}, \overline{\mathrm{b}}=3 \hat{\mathrm{i}}-\hat{\mathrm{j}}+2 \hat{\mathrm{k}}, \overline{\mathrm{c}}=\hat{\mathrm{i}}+3 \hat{\mathrm{j}}+\hat{\mathrm{k}}$$ and $$\overline{\mathrm{a}}+\lambda \overline{\mathrm{b}}$$ is perpendicular to $$\overline{\mathrm{c}}$$, then $$\lambda=$$

A
$$-$$2
B
4
C
$$-$$4
D
2
2
MHT CET 2021 21th September Evening Shift
+2
-0

If $${\pi \over 2} < \theta < \pi$$ and $$|\overline a | = 5,|\overline b | = 13,|\overline a \times \overline b | = 25$$, then the value of $$\overline a \,.\,\overline b$$ is

A
$$-$$12
B
60
C
$$-$$60
D
$$-$$13
3
MHT CET 2021 21th September Evening Shift
+2
-0

If $$|\bar{a} \times \bar{b}|^2+(\bar{a} \cdot \bar{b})^2=144$$ and $$|\bar{a}|=4$$, then $$|\bar{b}|=$$

A
8
B
12
C
3
D
16
4
MHT CET 2021 21th September Morning Shift
+2
-0

The distance between parallel lines

\begin{aligned} & \bar{r}=(2 \hat{i}-\hat{j}+\hat{k})+\lambda(2 \hat{i}+\hat{j}-2 \hat{k}) \text { and } \\ & \bar{r}=(\hat{i}-\hat{j}+2 \hat{k})+\mu(2 \hat{i}+\hat{j}-2 \hat{k}) \text { is } \end{aligned}

A
$$\sqrt{2}$$
B
$$\frac{1}{3}$$ units
C
$$\frac{1}{\sqrt{3}}$$ units
D
$$\frac{\sqrt{2}}{3}$$ units
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