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Mark against the correct answer in each of the following:

Question: Mark against the correct answer in each of the following: If the plane $2 x-y+z=0$ is parallel to the line $\frac{2 x-1}{2}=\frac{2-y}{2}=\frac{z+1}{a}$, then the value of $a$ is A. $-4$ B. $-2$ C. 4 D. 2 Solution:...

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Mark against the correct answer in each of the following:

Question: Mark against the correct answer in each of the following: The equation of the plane passing through the points $A(0,-1,0), B(2,1,-1)$ and $C(1,1,1)$ is given by A. $4 x+3 y-2 z-3=0$ B. $4 x-3 y+2 z+3=0$ C. $4 x-3 y+2 z-3=0$ D. None of these Solution:...

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Mark against the correct answer in each of the following:

Question: Mark against the correct answer in each of the following: The equation of the plane passing through the intersection of the planes $3 x-y+2 z-4=0$ and $x+y+z-2=0$ and passing through the point $A(2,2,1)$ is given by A. $7 x+5 y-4 z-8=0$ B. $7 x-5 y+4 z-8=0$ C. $5 x-7 y+4 z-8=0$ D. $5 x+7 y-4 z+8=0$ Solution:...

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Mark against the correct answer in each of the following:

Question: Mark against the correct answer in each of the following: The equation of the plane passing through the points $\mathrm{A}(2,2,1)$ and $\mathrm{B}(9,3,6)$ and perpendicular to the plane $2 x+6 y+6 z=1$, is A. $x+2 y-3 z+5=0$ B. $2 x-3 y+4 z-6=0$ C. $4 x+5 y-6 z+3=0$ D. $3 x+4 y-5 z-9=0$ Solution:...

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Mark against the correct answer in each of the following:

Question: Mark against the correct answer in each of the following: The line $\frac{x-1}{2}=\frac{y-2}{4}=\frac{z-3}{-3}$ meets the plane $2 x+3 y-z=14$ in the point A. $(2,5,7)$ B. $(3,5,7)$ C. $(5,7,3)$ D. $(6,5,3)$ Solution:...

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Mark against the correct answer in each of the following:

Question: Mark against the correct answer in each of the following: The equation of a plane through the point $A(1,0,-1)$ and perpendicular to the line $\frac{x+1}{2}=\frac{y+3}{4}=\frac{z+7}{-3}$ is A. $2 x+4 y-3 z=3$ B. $2 x-4 y+3 z=5$ C. $2 x+4 y-3 z=5$ D. $x+3 y+7 z=-6$ Solution:...

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Mark against the correct answer in each of the following:

Question: Mark against the correct answer in each of the following: If a plane meets the coordinate axes in $A, B$ and $C$ such that the centroid of $\triangle A B C$ is $(1,2,4)$, then the equation of the plane is A. $x+2 y+4 z=6$ B. $4 x+2 y+z=12$ C. $x+2 y+4 z=7$ D. $4 x+2 y+z=7$ Solution:...

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Mark against the correct answer in each of the following:

Question: Mark against the correct answer in each of the following: The plane $2 x+3 y+4 z=12$ meets the coordinate axes in $A, B$ and $C$. The centroid of $\triangle A B C$ is A. $(2,3,4)$ B. $(6,4,3)$ C. $\left(2, \frac{4}{3}, 1\right)$ D. None of these Solution:...

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Mark against the correct answer in each of the following:

Question: Mark against the correct answer in each of the following: If the line $\frac{x-4}{1}=\frac{y-2}{1}=\frac{z-k}{2}$ lies in the plane $2 x-4 y+z=7$, then the value of $k$ is A. $-7$ B. 7 C. 4 D. $-4$ Solution:...

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Mark against the correct answer in each of the following:

Question: Mark against the correct answer in each of the following: If $O$ is the origin and $P(1,2,-3)$ is a given point, then the equation of the plane through $P$ and perpendicular to OP is A. $x+2 y-3 z=14$ B. $x-2 y+3 z=12$ C. $x-2 y-3 z=14$ D. None of these Solution:...

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Mark against the correct answer in each of the following:

Question: Mark against the correct answer in each of the following: If the line $\frac{x+1}{3}=\frac{y-2}{4}=\frac{z+6}{5}$ is parallel to the plane $2 x-3 y+k z=0$, then the value of $k$ is A. $\frac{5}{6}$ B. $\frac{6}{5}$ C. $\frac{3}{4}$ D. $\frac{4}{5}$ Solution:...

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Mark against the correct answer in each of the following:

Question: Mark against the correct answer in each of the following: A plane cuts off intercepts $3,-4,6$ on the coordinate axes. The length of perpendicular from the origin to this plane is A. $\frac{5}{\sqrt{29}}$ units B. $\frac{8}{\sqrt{29}}$ units C. $\frac{6}{\sqrt{29}}$ units D. $\frac{12}{\sqrt{29}}$ units Solution:...

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Mark against the correct answer in each of the following:

Question: Mark against the correct answer in each of the following: The equation of a plane passing through the point $A(2,-3,7)$ and making equal intercepts on the axes, is A. $x+y+z=3$ B. $x+y+z=6$ C. $x+y+z=9$ D. $x+y+z=4$ Solution:...

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Mark against the correct answer in each of the following:

Question: Mark against the correct answer in each of the following: The length of perpendicular from the origin to the plane $\overrightarrow{\mathrm{r}} \cdot(3 \hat{\mathrm{i}}-4 \hat{\mathrm{j}}-12 \hat{\mathrm{k}})+39=0$ is A. 3 units B. $\frac{13}{5}$ units C. $\frac{5}{3}$ units D. None of these Solution:...

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Mark against the correct answer in each of the following:

Question: Mark against the correct answer in each of the following: The direction cosines of the normal to the plane $5 y+4=0$ are A. $0, \frac{-4}{5}, 0$ B. $0,1,0$ C. $0,-1,0$ D. None of these Solution:...

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Mark against the correct answer in each of the following:

Question: Mark against the correct answer in each of the following: The direction cosines of the perpendicular from the origin to the plane $\overrightarrow{\mathrm{r}} \cdot(6 \hat{\mathrm{i}}-3 \hat{\mathrm{j}}+2 \hat{\mathrm{k}})+1=0$ are A. $\frac{6}{7}, \frac{3}{7}, \frac{-2}{7}$ B. $\frac{6}{7}, \frac{-3}{7}, \frac{2}{7}$ C. $\frac{-6}{7}, \frac{3}{7}, \frac{2}{7}$ D. None of these Solution:...

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Write the equation of a plane passing through the point

Question: Write the equation of a plane passing through the point $(2,-1,1)$ and parallel to the plane $3 x+2 y-z=7$. Solution:...

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Write the angle between the line

Question: Write the angle between the line $\frac{x-1}{2}=\frac{y-2}{1}=\frac{z+3}{-2}$ and the plane $x+y+4=0$ Solution:...

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Solve this following

Question: Find the value of $\lambda$ for which the line $\frac{x-1}{2}=\frac{y-1}{3}=\frac{z-1}{2}$ is parallel to the plane $\bar{r} \cdot(2 \hat{\imath}+3 \hat{\jmath}+4 \hat{k})=4$ Solution:...

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Find the length of perpendicular from the origin to the plane

Question: Find the length of perpendicular from the origin to the plane $\bar{r} \cdot(2 \hat{j}-3 \hat{j}+6 \hat{k})+14-0$. Solution:...

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Solve this following

Question: Show that the line $\vec{r}-(4 \hat{i}-7 \hat{k})+\lambda(4 \hat{i}-2 \hat{j}+3 \hat{k})$ is parallel to the plane $\vec{r} \cdot(5 \hat{i}+4 \hat{j}-4 \hat{k})-7$. Solution: Hence, the given line is parallel to the given plane....

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Find the direction cosines of the perpendicular from the origin to the plane

Question: Find the direction cosines of the perpendicular from the origin to the plane $\bar{r} \cdot(6 \hat{i}-3 \hat{j}-2 \hat{k})+1-0$. Solution:...

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Find the length of perpendicular drawn from the origin to the plane

Question: Find the length of perpendicular drawn from the origin to the plane $2 x-3 y+6 z+21=0$. Solution:...

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Write the equation of the plane passing through the point

Question: Write the equation of the plane passing through the point $(\mathrm{a}, \mathrm{b}, \mathrm{c})$ and parallel to the plane $\bar{r} \cdot(\hat{i}+\hat{j}+\hat{k})=2$. Solution:...

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Solve this following

Question: Find the value of $\lambda$ such that the line $\frac{x-2}{6}=\frac{y-1}{2}=\frac{z+5}{4}$ is perpendicular to the plane $3 x-y-2 z=7$. Solution:...

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