1. ## Vectors

1.) Find the equation of the plane containing A(3,2,1) and the line x=1+t, y= 2-t, z = 3+2t

I know that there are two positional vectors, 3i+2j+k and i+2j+3k, and I know I have a vector equation..but what do I do? I thought of using dot product, but I don't know what I should dot..

2.) The perpendicular from a point to a line minimizes the distance from the point to that line.Use quadratic theory to find th ecoordinates of the foot of the perpendicular from (1,1,2) to the line with equations x=1+t, y=2-t, z=3+t

I really do not know how to do this one..

Thank you for your help, really would want to know how to solve these two questions, thanks so so much for your efforts in advance!

2. ## Re: Vectors

Tutu
Do not be so desperate..use your brain.... take two values for t (t=0) and t=1 and find two more points of the plane....for t=0 you will find that the point Q(1,2,3) lies on the plane and fot t=1 the point R(2,1,5) lies on the plane...then your problem is to find the equation of a plane given 3 points...easy....
the rest is really easy

MINOAS

3. ## Re: Vectors

Originally Posted by Tutu
1.) Find the equation of the plane containing A(3,2,1) and the line x=1+t, y= 2-t, z = 3+2t

2.) The perpendicular from a point to a line minimizes the distance from the point to that line.Use quadratic theory to find th ecoordinates of the foot of the perpendicular from (1,1,2) to the line with equations x=1+t, y=2-t, z=3+t

1) $\displaystyle t=0\text{ so }B(1,2,3)$ is a point on the line.
Let $\displaystyle N=\overrightarrow {BA} \times \left\langle {1, - 1,2} \right\rangle$.
Now you have a point and a normal. Write the equation of the plane.

2) If $\displaystyle P$ is a point not on line $\displaystyle \ell: Q+tD$ then the distance:
$\displaystyle \math{D}(P;\ell)=\frac{|\overrightarrow {QP}\times D|}{\|D\|}.$