The cartesian equation of a line is `3x+2=5y-4=3-z`.
Find a point on the line and its direction ratios, hence rewrite this equation in symmetric from and then reduce it to vector form.

Answer

`(-(2)/(3),(4)/(5),3);` direction ratios `(1)/(3),(1)/(5),-1;(x+(2)/(3))/((1)/(3))=(y-(4)/(5))/((1)/(5))=(z-3)/(-1)`;
`vec(r)=(-(2)/(3)hat(i)+(4)/(5)hat(j)+3hat(k))+t((1)/(3)hat(i)+(1)/(5)hat(j)-hat(k))`