91Ó°ÊÓ

Find the equations of the line passing through the point \((3,2,-8)\) and is perpendicular to the plane \(3 x-y-2 z+2=0\).

Prove that the equations of the normal to the plane \(a x+b y+c z+d=0\) through the point \((\alpha, \beta, \gamma)\) are \(\frac{x-\alpha}{a}=\frac{y-\beta}{b}=\frac{z-\gamma}{c}\).

Express in symmetrical form the following lines: (i) \(x+2 y+z=3,6 x+8 y+3 z=13\) (ii) \(x-2 y+3 z-4=0,2 x-3 y+4 z-5=0\) (iii) \(x+3 y-z-15=0.5 x-2 y+4 z+8=0\)

Find the foot of the perpendicular from the point \((-1,11,5)\) to the line \(\frac{x-2}{3}=\frac{y+3}{2}=\frac{z}{2}\)

Find the equation of the projection of the straight line \(\frac{x-1}{1}=\frac{y+1}{2}=\frac{z}{3}\) on the plane \(x+y+2 z=5\) in symmetrical form.