1
MHT CET 2022 11th August Evening Shift
+2
-0

Let $$\bar{a}=\hat{\mathbf{i}}-2 \hat{\mathbf{j}}+\hat{\mathbf{k}}$$ and $$\bar{b}=\hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}}$$ be two vectors. If $$\bar{c}$$ is a vector such that $$\bar{b} \times \bar{c}=\bar{b} \times \bar{a}$$ and $$\bar{c} \cdot \bar{a}=0$$, then $$\bar{c} \cdot \bar{b}$$ is equal to

A
$$-\frac{1}{2}$$
B
$$\frac{3}{2}$$
C
$$\frac{1}{2}$$
D
$$-\frac{3}{2}$$
2
MHT CET 2022 11th August Evening Shift
+2
-0

The magnitude of the projection of the vector $$2 \hat{\mathbf{i}}+ 3\hat{\mathbf{j}}+\hat{\mathbf{k}}$$ on the vector perpendicular to the plane containing the vectors $$\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}$$ and $$\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}$$ is

A
$$3 \sqrt{6}$$ units
B
$$\frac{\sqrt{3}}{2}$$ units
C
$$\frac{1}{\sqrt{6}}$$ units
D
$$\sqrt{\frac{3}{2}}$$ units
3
MHT CET 2022 11th August Evening Shift
+2
-0

If $$\bar{a}=\hat{\boldsymbol{i}}+\hat{\boldsymbol{j}}+\hat{\boldsymbol{k}}, \bar{b}=\hat{\boldsymbol{i}}-\hat{\boldsymbol{j}}+\hat{\boldsymbol{k}}$$ and $$\bar{c}=\hat{\boldsymbol{i}}-\hat{\boldsymbol{j}}-\hat{\boldsymbol{k}}$$ are three vectors then vector $$\bar{r}$$ in the plane of $$\bar{a}$$ and $$\bar{b}$$, whose projection on $$\bar{c}$$ is $$\frac{1}{\sqrt{3}}$$, is given by

A
$\hat{i}-3 \hat{j}+3 \hat{k}$
B
$-3 \hat{i}-3 \hat{j}-\hat{k}$
C
$3 \hat{i}-\hat{j}+3 \hat{k}$
D
$\hat{i}+3 \hat{j}-3 \hat{k}$
4
MHT CET 2022 11th August Evening Shift
+2
-0

The polar co-ordinates of the point, whose Cartesian coordinates are $$(-2 \sqrt{3}, 2)$$, are

A
$$\left(4,\left(\frac{3 \pi}{4}\right)\right)$$
B
$$\left(4,\left(\frac{5 \pi}{6}\right)\right)$$
C
$$\left(4,\left(\frac{2 \pi}{3}\right)\right)$$
D
$$\left(4,\left(\frac{11 \pi}{12}\right)\right)$$
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