Find symmetric and parametric equations of the line through
Find symmetric and parametric equations of the line through A(3,-7,1) which is perpendicular to the vectors a=-2i-j+3k and b=3i+3j+2k.
Solution
The direction vector is:
u = a x b = (-2i-j+3k) x (3i+3j+2k) =(-11i + 13j - 3k)
So the line equation is:
(3,-7,1) + t(-11 , 13 , -3)
The symmetric equation: (x-3)/(-11) = (y+7)/13 = (z-1)/(-3)
paametric equation = (-11t+3 , 13t-7 , -3t+1)
