Check if a line that passes through the points A102 and B231

Check if a line that passes through the points A(1,0,-2) and B(2,3,-1) is parallel to the plane with the parametric equation x=1+s+t, y=2-2s+t and z=3-2t.

Solution

Equation of line passing through A and B is (x-1)/(2-1) = (y-0)/(3-0) = (z+1)/-2

hence,

x -1 = y = z+1/ -2

Now, if you sub the value of x,y,z as x=1+s+t, y=2-2s+t and z=3-2t , you wiill see that the values don\'t match

Hence, for the given points aren\'t parallel line passing th through the points A(1,0,-2) and B(2,3,-1)