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

If $$\overline{\mathrm{a}}, \overline{\mathrm{b}} , \overline{\mathrm{c}}$$ are three vectors which are perpendicular to $$\overline{\mathrm{b}}+\overline{\mathrm{c}}, \overline{\mathrm{c}}+\overline{\mathrm{a}}$$ and $$\overline{\mathrm{a}}+\overline{\mathrm{b}}$$ respectively, such that $$|\bar{a}|=2,|\bar{b}|=3,|\bar{c}|=4$$, then $$|\bar{a}+\bar{b}+\bar{c}|=$$

A
29
B
3
C
9
D
$$\sqrt{29}$$
2
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
$$\frac{27}{2}, 3$$
3
MHT CET 2020 16th October Morning Shift
+2
-0

If the vectors $$\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}, \hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}}$$ and $$2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+m \hat{\mathbf{k}}$$ are coplanar, then $$m=$$

A
3
B
2
C
$$-$$3
D
$$-$$2
4
MHT CET 2020 16th October Morning Shift
+2
-0

The angles between the lines $$\mathbf{r}=(\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}})+\lambda(\hat{\mathbf{i}}+\hat{\mathbf{j}}+2 \hat{\mathbf{k}}) \text { and } \mathbf{r}=(3 \hat{\mathbf{i}}+\hat{\mathbf{k}})+\lambda^{\prime}(2 \hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}}), \lambda, \lambda^{\prime} \in \mathbf{R}$$ is

A
$$\cos ^{-1}\left(\frac{1}{5}\right)$$
B
$$\cos ^{-1}\left(\frac{2}{3}\right)$$
C
$$\cos ^{-1}\left(\frac{1}{3}\right)$$
D
$$\cos ^{-1}\left(\frac{1}{6}\right)$$
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