Find the vector and cartesian equation of a line passes through the points `(1,3,2)` and origin.

Explanation

Cartesian equation of a line passing through two given points
`(x-x_(1))/(x_(2) - x_(1))= (y - y_(1))/(y_(2) - y_(1)) = (z - z_(1))/(z_(2) - z_(1))`
Therefore equation of a line passing through `(0,0,0)` and `(1,3,2)` is
`(x-0)/(1-0) = (y-0)/(3-0) = (z-0)/(2-0)`
`rArr x/1 = y/3 = z/2`
Position vectors of points `(0 ,0,0)` and `(1,3,2)` are respectively.
`vecr_(1) = 0.hati+0.hatj+0.hatk = vec0`
and `vecr_(2) = hati+3hatj+2hatk`
Equation of a line passint through two points whose position vectros are `vecr_(1)` and `vecr_(2)` is
`vecr = vecr_(1) + lambda(vecr_(2) + vecr_(1))`
`rArr vecr = vec0+lambda(hati+3hatj+2hatk-hat0)`
`rArr vecr= lambda(hati+3hatj+2hatk)`