Embibe Experts Solutions for Exercise 4: EXERCISE 12.4

Find the image of the point $P\left(3,5,7\right)$ in the plane $2x+y+z=0$.

Find the equation of the line of intersection of the planes $4x+4y-5z=12,8x+12y-13z=32$ in the symmetric form.

The equation of the plane passing through the points $\left(0,-1,-1\right),\left(-4,4,4\right)$ and $\left(4,5,1\right)$ is given by

A variable plane moves in such a way that the sum of reciprocals of its intercepts on the three co-ordinate axes is constant. Show that the plane passes through the fixed point.

Find the vector equation of a plane which is at a distance of $8$ units from the origin and which is normal to the vector $2\hat{i}+\hat{j}+2\hat{k}$.

Reduce the equation $\overrightarrow{r}·\left(3\hat{i}-4\hat{j}+12\hat{k}\right)=5$ to normal form and hence, find the length of perpendicular from the origin to the plane.

Find equation of the plane passing through the points $P\left(1,1,1\right), Q\left(3,-1,2\right), R\left(-3,5,-4\right)$.

The line of intersection of the planes $\overrightarrow{r}·\left(3\hat{i}-\hat{j}+\hat{k}\right)=1$ and $\overrightarrow{r}·\left(\hat{i}+4\hat{j}-2\hat{k}\right)=2$ is parallel to the vector