1
MHT CET 2023 9th May Morning Shift
+2
-0

A vector $$\overrightarrow{\mathrm{n}}$$ is inclined to $$\mathrm{X}$$-axis at $$45^{\circ}$$, $$\mathrm{Y}$$-axis at $$60^{\circ}$$ and at an acute angle to Z-axis If $$\overrightarrow{\mathrm{n}}$$ is normal to a plane passing through the point $$(-\sqrt{2}, 1,1)$$, then equation of the plane is

A
$$\sqrt{2} x+y+z=0$$
B
$$x+\sqrt{2} y+z=1$$
C
$$-\sqrt{2} x+y+2 z=5$$
D
$$x+y+\sqrt{2} z=1$$
2
MHT CET 2023 9th May Morning Shift
+2
-0

If the Cartesian equation of a line is $$6 x-2=3 y+1=2 z-2$$, then the vector equation of the line is

A
$$\overline{\mathrm{r}}=\left(\frac{1}{3} \hat{\mathrm{i}}-\frac{1}{3} \hat{\mathrm{j}}+\hat{\mathrm{k}}\right)+\lambda(\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+3 \hat{\mathrm{k}})$$
B
$$\overline{\mathrm{r}}=(\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}})+\lambda(\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+3 \hat{\mathrm{k}})$$
C
$$\overline{\mathrm{r}}=\left(\frac{-1}{3} \hat{\mathrm{i}}+\frac{1}{3} \hat{\mathrm{j}}+\hat{\mathrm{k}}\right)+\lambda(\hat{\mathrm{i}}-2 \hat{\mathrm{j}}+3 \hat{\mathrm{k}})$$
D
$$\overline{\mathrm{r}}=\left(\frac{1}{3} \hat{\mathrm{i}}-\frac{1}{3} \hat{\mathrm{j}}-\hat{\mathrm{k}}\right)+\lambda(\hat{\mathrm{i}}-\hat{\mathrm{j}}+\hat{\mathrm{k}})$$
3
MHT CET 2022 11th August Evening Shift
+2
-0

The distance between parallel lines

$$\frac{x-1}{2}=\frac{y-2}{-2}=\frac{z-3}{1}$$ and

$$\frac{x}{2}=\frac{y}{-2}=\frac{z}{1}$$ is :

A
$$\frac{2 \sqrt{5}}{3}$$ units
B
$$\frac{\sqrt{5}}{3}$$ units
C
$$\frac{5 \sqrt{5}}{3}$$ units
D
$$\frac{4 \sqrt{5}}{3}$$ units
4
MHT CET 2022 11th August Evening Shift
+2
-0

A line makes the same angle '$$\alpha$$' with each of the $$x$$ and $$y$$ axes. If the angle '$$\theta$$', which it makes with the $$z$$-axis, is such that $$\sin ^2 \theta=2 \sin ^2 \alpha$$, then the angle $$\alpha$$ is

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