Vector Equation of a Line, given points to find scalar value
I cannot locate the triangle that should report this post. But I searched Vectors in threads and in posts and vector problems show up under calculus. I have also decided to post my vector problem under here because I am taking a Calculus and Vectors course.
The points A(1,2,3) and B(3,-1,6) lie on the lin L.
a) Find an equation for the line L in the form r=a+tb.
b) Write down a vector in the direction of the line.
The point P has position vector OP=(x y z) <-- in column vector format, and OP is perpendicular to the line L.
c) Show that 2x-3y+3z=0
The point P lies on the line L.
d) Show that, at point P, t= -5/22
I've included the whole question for context, I am struggling with d)
What I have done is equate vector AP with vector AB and attached 't' to AB, but I do not know where to go from there or if I am even on the right track. What is an efficient way to show t?