Question

[Calc III] Let P be a point not on the line L that passes through the points Q and R. The distance d from the point P to the line L is d= abs. val.[(a [cross] b)]/abs. val. (a) where a = QR(vector) and b = QP(vector). Use this formula to find the distance from the point (-4,1,-3) the the line: x=-3+t, y=4-4t, z=2t.

Answer 1

rewritten more clearly, the distance d from point P to the line L is \[d=\left| a x b \right|/\left| a \right| \]

Answer 2

the formula for distance from a point to a line is d=\[\left| \right|LXP _{0}P_{1}\left| \right|/ \left| \right|L \left| \right|\] With L as the vector parallel to the line p0 on l and p1 the point not on l

Answer 3

i'm just not sure how to find QP, i found that QR is <1,-4,2> using the paramentric equations, but i'm not given Q, so i can't make a vector out of QP