Find the equation of the plane through the line of intersection of the planes
Question: Find the equation of the plane through the line of intersection of the planes $x-3 y+z+6=0$ and $x+2 y+3 z+5=0$, and passing through the origin. Solution:...
Read More →Find the equation of the plane through the line of intersection of the planes
Question: Find the equation of the plane through the line of intersection of the planes $x+y+z=6$ and $2 x+2 y+4 z+5=0$, and passing through the point (1, 1, 1). Solution:...
Read More →Find the distance between the planes
Question: Find the distance between the planes $x+2 y+3 z+7=0$ and $2 x+4 y+6 z+7=0$. Solution:...
Read More →Find the equations of planes parallel to the plane
Question: Find the equations of planes parallel to the plane $x-2 y+2 z=3$ which are at a unit distance from the point ( $1,2,3$ ). Solution:...
Read More →Find the equations of the plane passing through the point
Question: Find the equations of the plane passing through the point $(-1,0,7)$ and parallel to the plane $3 x-5 y+4 z=11$. Solution:...
Read More →Find the equations of the plane passing through the origin and parallel to the plane
Question: Find the equations of the plane passing through the origin and parallel to the plane $2 x-3 y+7 z+13=0$. Solution:...
Read More →Find the equation of the plane passing through the point
Question: Find the equation of the plane passing through the point $(1,4,-2)$ and parallel to the plane $2 x-y+3 z+7=0$. Solution:...
Read More →Find the vector equation of the plane passing through the point
Question: Find the vector equation of the plane passing through the point $(1,1,1)$ and parallel to the plane $\overrightarrow{\mathrm{r}} \cdot(2 \hat{\mathrm{i}}-\hat{\mathrm{j}}+2 \hat{\mathrm{k}})=5$. Solution:...
Read More →Find the vector equation of the plane passing through the point
Question: Find the vector equation of the plane passing through the point $(\mathrm{a}, \mathrm{b}, \mathrm{b})$ and parallel to the plane $\overrightarrow{\mathrm{r}} \cdot(\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}})=2$. There is a error in question the point should be $(a, b, c)$ instead of $(a, b, b)$ to get the required answer. Solution:...
Read More →Find the vector equation of the plane through the point
Question: Find the vector equation of the plane through the point $(3 \hat{\mathrm{i}}+4 \hat{\mathrm{j}}-\hat{\mathrm{k}})$ and parallel to the plane $\overline{\mathrm{r}} \cdot(2 \hat{\mathrm{i}}-3 \hat{\mathrm{j}}+5 \hat{\mathrm{k}})+5=0$. Solution:...
Read More →Solve this following
Question: Show that the planes $2 x-y+6 z=5$ and $5 x-2.5 y+15 z=12$ are parallel. Solution:...
Read More →Find the equation of the plane mid-parallel to the planes
Question: Find the equation of the plane mid-parallel to the planes $2 x-3 y+6 z+21=0$ and $2 x-3 y+6 z-14=0$ Solution:...
Read More →Find the equation of the plane parallel to the plane
Question: Find the equation of the plane parallel to the plane $2 x-3 y+5 z+7=0$ and passing through the point ( 3 , 4 , $-1$ ). Also, find the distance between the two planes. Solution:...
Read More →Find the equation of the planes parallel to the plane
Question: Find the equation of the planes parallel to the plane $x-2 y+2 z-3=0$, each one of which is at a unit distance from the point $(1,1,1)$. Solution:...
Read More →Find the distance between the parallel planes
Question: Find the distance between the parallel planes $x+2 y-2 z+4=0$ and $x+2 y-2 z-8=0$. Solution:...
Read More →Find the distance between the parallel planes
Question: Find the distance between the parallel planes $2 x+3 y+4=4$ and $4 x+6 y+8 z=12$. Solution:...
Read More →Solve this following
Question: Show that the points $(-3,0,1)$ and $(1,1,1)$ are equidistant from the plane $3 x+4 y-12 z+13=0$. Solution:...
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Question: Show that the point $(1,2,1)$ is equidistant from the planes $\vec{r} \cdot(\hat{i}+2 \hat{j}-2 \hat{k})=5$ and $\vec{r} \cdot(2 \hat{i}-2 \hat{j}+\hat{k})+3=0$. Solution:...
Read More →Solve this following
Question: Find the distance of the point $(2,1,-1)$ from the plane $x-2 y+4 z=9$ Solution:...
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Question: Find the distance of the point $(2,1,0)$ from the plane $2 x+y+2 z+5=0$ Solution:...
Read More →Find the distance of the point
Question: Find the distance of the point $(1,1,2)$ from the plane $\overrightarrow{\mathrm{r}} \cdot(2 \hat{\mathrm{i}}-2 \hat{\mathrm{j}}+4 \hat{\mathrm{k}})+5=0$. Solution:...
Read More →Solve this following
Question: Find the distance of the point $(3,4,5)$ from the plane $\overrightarrow{\mathrm{r}} \cdot(2 \hat{\mathrm{i}}-5 \hat{\mathrm{j}}+3 \hat{\mathrm{k}})=13$. Solution:...
Read More →Solve this following
Question: Find the distance of the point $(\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+5 \hat{\mathrm{k}})$ from the plane $\overrightarrow{\mathrm{r}} \cdot(\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}})+17=0$. Solution:...
Read More →Find the distance of the point
Question: Find the distance of the point $(2 \hat{\mathrm{i}}-\hat{\mathrm{j}}-4 \hat{\mathrm{k}})$ from the plane $\overrightarrow{\mathrm{r}} \cdot(3 \hat{\mathrm{i}}-4 \hat{\mathrm{j}}+12 \hat{\mathrm{k}})=9$. Solution:...
Read More →Find the vector equation of a line passing through the point
Question: Find the vector equation of a line passing through the point $(2 \hat{i}-3 \hat{j}-5 \hat{k})$ and perpendicular to the plane $\vec{r} \cdot(6 \hat{i}-3 \hat{j}+5 \hat{k})+2-0$. Also, find the point of intersection of this line and the plane. Solution:...
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