MHT CET 2021 20th September Evening Shift | Three Dimensional Geometry Question 97 | Mathematics

The Cartesian equation of the plane $$\overline{\mathrm{r}}=(\hat{\mathrm{i}}-\hat{\mathrm{j}})+\lambda(\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}})+\mu(\hat{\mathrm{i}}-2 \hat{\mathrm{j}}+3 \hat{\mathrm{k}})$$ is

$$x+y+z=0$$

$$5 x+2 y+3 z=3$$

$$2 x+y+z=0$$

$$5 x-2 y-3 z-7=0$$

MHT CET 2021 20th September Evening Shift

MCQ (Single Correct Answer)

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The equation of the plane that contains the line of intersection of the planes. $$x+2 y+3 z-4=0$$ and $$2 x+y-z+5=0$$ and is perpendicular to the plane $$5 x+3 y-6 z+8=0$$ is

$$14 x+7 y-7 z-4=0$$

$$33 x+45 y+50 z-41=0$$

$$-33 x+45 y-50 z+41=0$$

$$5 x+31 y+50 z-41=0$$

MHT CET 2021 20th September Evening Shift

MCQ (Single Correct Answer)

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The vector equation of the line whose Cartesian equations are y = 2 and 4x $$-$$ 3z + 5 = 0 is

$$\overline{\mathrm{r}}=(2 \hat{\mathrm{j}}+\hat{\mathrm{k}})+\lambda(3 \hat{\mathrm{i}}-4 \hat{\mathrm{k}})$$

$$\overline{\mathrm{r}}=\left(2 \hat{\mathrm{j}}+\frac{5}{3} \hat{\mathrm{k}}\right)+\lambda(3 \hat{\mathrm{i}}+4 \hat{\mathrm{k}})$$

$$\bar{r}=(2 \hat{i}+\hat{k})+\lambda(3 \hat{i}+4 \hat{j})$$

$$\overline{\mathrm{r}}=\left(2 \hat{\mathrm{j}}+\frac{5}{3} \hat{\mathrm{k}}\right)+\lambda(3 \hat{\mathrm{i}}-4 \hat{\mathrm{k}})$$

MHT CET 2021 20th September Morning Shift

MCQ (Single Correct Answer)

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The Cartesian equation of the plane passing through the point $$(0,7,-7)$$ and containing the line $$\frac{x+1}{-3}=\frac{y-3}{2}=\frac{z+2}{1}$$ is

$$2 x+y-z=14$$

$$x+2 y+z=7$$

$$x+y+z=0$$

$$2 x+y+z=0$$

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