1
MHT CET 2021 23rd September Evening Shift
+2
-0

Let $$\overline{\mathrm{a}}=2 \hat{\mathrm{i}}+\hat{\mathrm{j}}-2 \hat{\mathrm{k}}$$ and $$\overline{\mathrm{b}}=\hat{\mathrm{i}}+\hat{\mathrm{j}}$$. If $$\overline{\mathrm{c}}$$ is a vector such that $$\overline{\mathrm{a}} \cdot \overline{\mathrm{c}}=|\overline{\mathrm{c}}|,|\overline{\mathrm{c}}-\overline{\mathrm{a}}|=2 \sqrt{2}$$ and the angle between $$\overline{\mathrm{a}} \times \overline{\mathrm{b}}$$ and $$\overline{\mathrm{c}}$$ is $$60^{\circ}$$. Then $$|(\overline{\mathrm{a}} \times \overline{\mathrm{b}}) \times \overline{\mathrm{c}}|=$$

A
$$\frac{3 \sqrt{3}}{2}$$
B
$$\frac{3}{2}$$
C
$$3 \sqrt{3}$$
D
$$\frac{\sqrt{3}}{2}$$
2
MHT CET 2021 23rd September Evening Shift
+2
-0

The projection of $$\bar{a}=\hat{i}-2 \hat{j}+\hat{k}$$ on $$\bar{b}=2 \hat{i}-\hat{j}+\hat{k}$$ is

A
5
B
$$5 \sqrt{6}$$
C
$$\frac{5}{\sqrt{6}}$$
D
$$\sqrt{6}$$
3
MHT CET 2021 23rd September Evening Shift
+2
-0

If $$\bar{a}=2 \hat{i}-\hat{j}+\hat{k}, \bar{b}=\hat{i}+2 \hat{j}-3 \hat{k}$$ and $$\bar{c}=3 \hat{i}+\lambda \hat{j}+5 \hat{k}$$ are coplanar, then $$\lambda$$ is the root of the equation

A
$$\mathrm{x}^2+3 \mathrm{x}=6$$
B
$$x^2+2 x=4$$
C
$$x^2+3 x=4$$
D
$$x^2+2 x=6$$
4
MHT CET 2021 23th September Morning Shift
+2
-0

If $$\hat{a}$$ is a unit vector such that $$(\bar{x}-\hat{a}) \cdot(\bar{x}+\hat{a})=8$$, then $$|\bar{x}|=$$

A
$$\pm 3$$
B
$$2 \sqrt{2}$$
C
3
D
$$\pm \sqrt{7}$$
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