MHT CET 2023 11th May Morning Shift | Three Dimensional Geometry Question 110 | Mathematics

A plane is parallel to two lines, whose direction ratios are $$1,0,-1$$ and $$-1,1,0$$ and it contains the point $$(1,1,1)$$. If it cuts co-ordinate axes $$(\mathrm{X}, \mathrm{Y}, \mathrm{Z}$$ - axes resp.) at $$\mathrm{A}, \mathrm{B}, \mathrm{C}$$, then the volume of the tetrahedron $$\mathrm{OABC}$$ is _________ cu. units.

$$\frac{9}{4}$$

$$\frac{9}{2}$$

MHT CET 2023 11th May Morning Shift

MCQ (Single Correct Answer)

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The lines $$\frac{x-1}{3}=\frac{y+1}{2}=\frac{z-1}{5} \quad$$ and $$\frac{x+2}{4}=\frac{y-1}{3}=\frac{z+1}{2}$$

intersect each other and point of intersection is $$(2,1,3)$$

intersect each other and point of intersection is $$(3,2,4)$$

intersect each other and point of intersection is $$(-2,3,3)$$

do not intersect.

MHT CET 2023 11th May Morning Shift

MCQ (Single Correct Answer)

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The vector equation of the line $$2 x+4=3 y+1=6 z-3$$ is

$$\overline{\mathrm{r}}=\left(2 \hat{\mathrm{i}}+\frac{1}{3} \hat{\mathrm{j}}+\frac{1}{2} \hat{\mathrm{k}}\right)+\lambda(3 \hat{\mathrm{i}}+2 \hat{\mathrm{j}}+\overline{\mathrm{k}})$$

$$\overline{\mathrm{r}}=\left(-2 \hat{\mathrm{i}}-\frac{1}{3} \hat{\mathrm{j}}+\frac{1}{2} \hat{\mathrm{k}}\right)+\lambda(3 \hat{\mathrm{i}}+2 \hat{\mathrm{j}}+\hat{\mathrm{k}})$$

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

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

MHT CET 2023 10th May Evening Shift

MCQ (Single Correct Answer)

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The plane through the intersection of planes $$x+y+z=1$$ and $$2 x+3 y-z+4=0$$ and parallel to $$\mathrm{Y}$$-axis also passes through the point

$$(3,3,-1)$$

$$(-3,0,1)$$

$$(3,2,1)$$

$$(-3,0,-1)$$

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