Find the vector and Cartesian equations of the line joining the points whose position vectors are `(hat(i) -2hat(j) +hat(k)) " and " (hat(i) +3hat(j) -2hat(k))`

Answer

`vec(r )=(hat(i) -2hat(j)+hat(k)) +lambda(5hat(j) -3hat(k)),(x-1)/(0)=(y+2)/(5) +(z-1)/(-3)`

Explanation

The given lines passes through the point A(3,-2,1) and it has d.r.'s (2+2) ,(3 -4) (-2 -1) i.e., 0,5,-3
So, its vector equations is `vec( r) =(hat(i) -2hat(j) +hat(k)) +lambda (5hat(j) -3hat(k))`
And its Cartesian equations are `(x-1)/(0)=(y+2)/(5)=(z-1)/(-3)`