## Find the angle between the line

Question: Find the angle between the line $\bar{r}-(\hat{i}+\hat{j}-2 \hat{k})+\lambda(\hat{i}-\hat{j}+\hat{k})$ and the plane $\bar{r} \cdot(2 \hat{i}-\hat{j}+\hat{k})=4$. Solution:...

Read More →## Find the angle between the line

Question: Find the angle between the line $\frac{x-1}{2}=\frac{y}{3}=\frac{z-3}{6}$ and the planes $10 x+2 y-11 z=3$. Solution:...

Read More →## Find the angle between the planes

Question: Find the angle between the planes $\bar{r} \cdot(3 \hat{i}-4 \hat{j}+5 \hat{k})=0$ and $\bar{r} \cdot(2 \hat{i}-\hat{j}-2 \hat{k})=7$. Solution:...

Read More →## Find the angle between the planes

Question: Find the angle between the planes $\bar{r} \cdot(\hat{i}+\hat{j})=1$ and $\bar{r} \cdot(\hat{i}+\hat{k})=3$. Solution:...

Read More →## Find the angle between the planes

Question: Find the angle between the planes $2 x+y-2 z=5$ and $3 x-6 y-2 z=7$. Solution:...

Read More →## Write the value of k for which the planes

Question: Write the value of $k$ for which the planes $2 x-5 y+k z=4$ and $x+2 y-z=6$ are perpendicular to each other. Solution:...

Read More →## Find the equation of a plane passing through the points

Question: Find the equation of a plane passing through the points $A(a, 0,0), B(0, b, 0)$ and $C(0,0, c)$. Solution:...

Read More →## Solve this following

Question: Reduce the equation $2 x-3 y+5 z+4=0$ to intercept form and find the intercepts made by it on the coordinate axes. Solution:...

Read More →## Write the intercepts made by the plane

Question: Write the intercepts made by the plane $4 x-3 y+2 z=12$ on the coordinate axes. Solution: Given:...

Read More →## Write the intercept cut off by the plane

Question: Write the intercept cut off by the plane $2 x+y-z=5$ on the $x$-axis. Solution:...

Read More →## Write the general equation of a plane parallel

Question: Write the general equation of a plane parallel to the $x$-axis. Solution:...

Read More →## Write the equation of the plane parallel

Question: Write the equation of the plane parallel to YZ-plane and passing through the point $(-3,2,0)$. Solution:...

Read More →## Write the equation of the plane parallel to

Question: Write the equation of the plane parallel to $X Y$-plane and passing through the point $(4,-2,3)$. Solution:...

Read More →## Find the direction cosines of the normal to the plane

Question: Find the direction cosines of the normal to the plane $3 x+4=0$. Solution:...

Read More →## Find the direction cosines of the normal to the plane

Question: Find the direction cosines of the normal to the plane $y=3$. Solution:...

Read More →## Find the direction cosines of the normal to the plane

Question: Find the direction cosines of the normal to the plane $2 x+3 y-z=4$. Solution:...

Read More →## Find the direction ratios of the normal to the plane

Question: Find the direction ratios of the normal to the plane $x+2 y-3 z=5$. Solution:...

Read More →## Find the equation of the plane which contains two parallel lines given

Question: Find the equation of the plane which contains two parallel lines given by $\frac{x-3}{1}=\frac{y-2}{-4}=\frac{z}{5}$ and $\frac{x-4}{1}=\frac{y-3}{-4}=\frac{z-2}{5}$. Solution:...

Read More →## Solve this following

Question: Show that the lines $\frac{x-1}{2}=\frac{y-3}{-1}=\frac{z}{-1}$ and $\frac{x-4}{3}=\frac{y-1}{-2}=\frac{z-1}{-1}$ are coplanar. Also find the equation of the plane containing these lines. Solution:...

Read More →## Solve this following

Question: Show that the lines $\frac{x-1}{-3}=\frac{y-3}{2}=\frac{z-2}{1}$ and $\frac{x}{1}=\frac{y-7}{-3}=\frac{z+7}{2}$ are coplanar. Find the equation of the plane containing these lines. Solution:...

Read More →## Solve this following

Question: Show that the lines $\frac{5-x}{-4}=\frac{y-7}{4}=\frac{z-3}{-5}$ and $\frac{x-8}{7}=\frac{2 y-8}{2}=\frac{z-5}{3}$ are coplanar. Find the equation of the plane containing these lines. Solution:...

Read More →## Solve this following

Question: Prove that the lines $\frac{x-2}{1}=\frac{y-4}{4}=\frac{z-6}{7}$ and $\frac{x+1}{3}=\frac{y+3}{5}=\frac{z+5}{7}$ are coplanar. Also find the equation of the plane containing these lines. Solution:...

Read More →## Solve this following

Question: Prove that the lines $\frac{x}{1}=\frac{y-2}{2}=\frac{z+3}{3}$ and $\frac{x-2}{2}=\frac{y-6}{3}=\frac{z-3}{4}$ are coplanar. Also find the equation of the plane containing these lines. Solution:...

Read More →## Find the vector and Cartesian equations of a plane containing the two lines

Question: Find the vector and Cartesian equations of a plane containing the two lines $\bar{r}=(2 \hat{i}+\hat{j}-3 \hat{k})+2(\hat{i}+2 \hat{j}+5 \hat{k})$ and $\bar{r}=(3 \hat{i}+3 \hat{j}+2 \hat{k})+\mu(3 \hat{i}-2 \hat{j}+5 \hat{k})$. Also show that the lines $\bar{r}=(2 \hat{i}+5 \hat{j}+2 \hat{k})+\rho(3 \hat{i}-2 \hat{j}+5 \hat{k})$ lies in the plane. Solution:...

Read More →## Find the vector and Cartesian forms of the equations of the plane containing the two lines

Question: Find the vector and Cartesian forms of the equations of the plane containing the two lines $\bar{r}=(\hat{i}+2 \hat{j}-4 \hat{k})+\lambda(2 \hat{i}+3 \hat{j}+6 \hat{k})$ and $\bar{r}=(9 \hat{i}+5 \hat{j}-\hat{k})+\mu(-2 \hat{i}+3 \hat{j}+8 \hat{k}) \ldots$ Solution:...

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