Question

Find a vector equation for the line through the point p = (5, 0, 0) and parallel to the vector v = (5, 3, -1). Assume ]and that v is the velocity vector of the line..

Answer 1

Answer- r(t) = (5,0,0) + t(5,3,-1)

Solution - we have been given the point vector P as (5,0,0) and the velocity vector V as (5,3,-1)

The general form for the vector equation of a line is (x,y,z) =         \

(Px, Py, Pz) + t(Vx, Vy, Vz)

Where P is a point, V is a vector and t is a scalar parameter.

Therefore, the vector equation of the requested line is:  

r(t) = r(x,y,z) =  (5,0,0) + t(5,3,-1)