Question

The line through the point (1,0,6) and perpendicular to the plane $x+3y+z=5$ has vector equation $\mathbf{r}=( u,v,w )=( a,b,c )+ t (d,e,f )$ where t is a parameter.

Making use of the parameter t, find the values of: u; v and w

Answer 1

$$r=(1,0,6)+t(1,3,1)=(u,v,w)$$

$$u=1+t, v=3t, w=6+t$$