Parametric equations for a line through two points and plane through three points

[brinlin]

Let P (1, 2, 3), Q (2, 3, 1), and R (3, 1, 2).
(a) Derive the parametric equations for the line that passes through P and Q without resorting
to the known formula.
(b) Derive the equation of the plane that passes through the points P, Q, and R without
resorting to the known formula.
(c) Find the area of the triangle with vertices P, Q, and R.

 

[skeeter]

(a) initial point + (direction vector) times t

(b) Calculus III - Equations of Planes (lamar.edu)

(c) area = $\dfrac{1}{2} |\vec{PQ} \times \vec{PR} |$

 

[Prove It]

(a) initial point + (direction vector) times t

(b) Calculus III - Equations of Planes (lamar.edu)

(c) area = $\dfrac{1}{2} |\vec{PQ} \times \vec{PR} |$

And I would hope that the OP would have found $\displaystyle \vec{PQ} \times \vec{PR}$ in part b) :P

 

[skeeter]

And I would hope that the OP would have found $\displaystyle \vec{PQ} \times \vec{PR}$ in part b) :p

seeing how the OP has posted the same problems on two other math help sites, I would hope so, also

 

[HOI]

It is not clear to me whether the OP's problem is with math or with reading English. He does not appear to have read, or understood, the instructions for this board. He has posted 8 or more threads without showing any attempt to solve them himself. I feel that I, at least, have already done too much.