1
MHT CET 2021 22th September Morning Shift
+2
-0

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

A
$$\bar{\mathrm{r}}=\left(\frac{-1}{3} \hat{\mathrm{i}}+\frac{1}{3} \hat{\mathrm{j}}+\hat{\mathrm{k}}\right)+\lambda(2 \hat{\mathrm{i}}-\hat{\mathrm{j}}-6 \hat{\mathrm{k}})$$
B
$$\bar{r}=(-\hat{i}+2 \hat{j}-\hat{k})+\lambda(3 \hat{i}+6 \hat{j}-\hat{k})$$
C
$$\bar{r}=\left(\frac{-1}{3} \hat{i}+\frac{1}{3} \hat{j}+\hat{k}\right)+\lambda(2 \hat{i}-\hat{j}+6 \hat{k})$$
D
$$\bar{\mathrm{r}}=\left(\frac{-1}{3} \hat{\mathrm{i}}+\frac{1}{3} \hat{\mathrm{j}}+\hat{\mathrm{k}}\right)+\lambda(2 \hat{\mathrm{i}}+\hat{\mathrm{j}}-6 \hat{\mathrm{k}})$$
2
MHT CET 2021 22th September Morning Shift
+2
-0

The plane $$\frac{x}{2}+\frac{y}{3}+\frac{z}{4}=1$$ cuts the $$X$$-axis at A, Y-axis at B and Z-axis at C, then the area of $$\triangle \mathrm{ABC}=$$

A
$$\sqrt{71}$$ sq. units
B
$$\sqrt{29}$$ sq. units
C
$$\sqrt{41}$$ sq. units
D
$$\sqrt{61}$$ sq. units
3
MHT CET 2021 22th September Morning Shift
+2
-0

If a plane meets the axes $$\mathrm{X}, \mathrm{Y}, \mathrm{Z}$$ in $$\mathrm{A}, \mathrm{B}, \mathrm{C}$$ respectively such that centroid of $$\triangle \mathrm{ABC}$$ is $$(1,2,3)$$, then the equation of the plane is

A
$$x+2 y+3 z=1$$
B
$$x+\frac{y}{2}+\frac{z}{3}=3$$
C
$$\frac{x}{3}+\frac{y}{6}+\frac{z}{9}=1$$
D
$$\frac{x}{4}+\frac{y}{8}+\frac{z}{12}=1$$
4
MHT CET 2021 22th September Morning Shift
+2
-0

The shortest distance between lines $$\bar{r}=(2 \hat{i}-\hat{j})+\lambda(2 \hat{i}+\hat{j}-3 \hat{k})$$ and $$\bar{r}=(\hat{r}-\hat{j}+2 \hat{k})+\mu(2 \hat{i}+\hat{j}-5 \hat{k})$$ is

A
$$\frac{1}{\sqrt{5}}$$
B
3 units
C
$$\sqrt{5}$$ units
D
2 units
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