Thread: Just need help with this vector question

1. Just need help with this vector question

i forgot the whole process, i know that for the second part since they are parallel they have the same normal its just i guess i use the point they gave me. but i still dont know how to get the scalar eqn with that. and for the first 1 im lost, can some 1 shine light on this please? i need to know ASAP so i can complete my hmwk on vectors.

Determine scalar, vector, and parametric eqns for the plane that passes through the points A(1,-2,0), B(1,-2,2), and C(0,3,2)

Write a scalar eqn for the plane that contains the point (-1,2,0) and is parallel to the plane (x,y,z) = (1,-2,1) + s(3,1,1) + t(4,-2,1)

2. First the first one, you can get two vectors in the plane by doing: B - A and C - A:

$\displaystyle B - A = <0, 0 , 2>$
$\displaystyle C - A = <-1, 5, 2>$

Then cross these 2 vectors to get a normal vector to the plane:

$\displaystyle <0, 0 , 2> X <-1, 5, 2> = <-10, -2, 0>$

Use this normal vector setup an equation with A(1,-2,0):

$\displaystyle -10(x - 1) - 2(y + 2) + 0(z - 0) = 0$
$\displaystyle -10x - 2y = -6$

For the second one, it's a similar problem:

Find 3 points in the plane by plugging in any numbers for s and t. Use those 3 points to find 2 vectors in the plane, cross them like the first problem, this gives you a normal vector, then setup a plane equation for the other plane using the point they give you: (-1,2,0).

3. thanks i solved the first 1, i just am having trouble with the second 1

4. Can I see your work for the second one?