Embibe Experts Solutions for Exercise 7: Assignment

The plane $\overrightarrow{r}·\overrightarrow{n}=q$ will contain the line $\overrightarrow{r}=\overrightarrow{a}+\lambda \overrightarrow{b}$ if

The projection of the line segment joining the points $\left(1,2,3\right)$ and $\left(4,5,6\right)$ on the plane $2x+y+z=1$ is

The line $x+2y-z-3=0=x+3y-z-4$ is parallel to

The shortest distance between the lines $x=y=z$ and the line $2x+y+z-1=0=3x+y+2z-2$ is

The plane containing the two lines $\frac{x-3}{1}=\frac{y-2}{4}=\frac{z-1}{5}$ and $\frac{x-2}{1}=\frac{y+3}{-4}=\frac{z+1}{29}$ is $17x+my+nz=P$, then $\left(m+n+P\right)$ is equal to

The positive value of $k$ for which the planes $x-y+z+1=0$, $kx+3y+2z-3=0$ and $3x+ky+z-2=0$ form a triangular prism must be equal to

The volume of tetrahedron formed by planes whose equations are $y+z=0, z+x=0, x+y=0$ and $x+y+z=1$ is $\lambda$ cubic units, then $9\lambda$ is equal to

Locus of the point, the sum of the square of whose distance from the planes $x+y+z=0, x-z=0$ and $x-2y+z=0$ is $9$ is $x^2+y^2+z^2=P$, then $P$ is equal to