Homework Statement
Find a necessary condition for the three planes given below to have a line of intersection.
-x +ay+bz=0
ax-y+cz=0
bx+cy-z=0
Homework Equations
in order to get a line of intersection between the planes..i know i need one line of the matrix to be [0 0 0|0]...
Thanks for the help so far
This is what I have done so far
I know that the plane is 2x-y+z=11
Therefore all line perpindicular to that plane have a direction of (2,-1,1)
The parametric equation of the line which passes through point P and hits the plane are
x=-1+2t
y=3-t
z=4+t
I...
Homework Statement
The point Q is the reflection of P(-1,3,4), in the plane with equation 2x-y+z=1.
Determine the coordinates of Q
Homework Equations
The Attempt at a Solution
Well I am not really looking for a solution. I just want to know what I am trying to find. What is a reflection in...
couple questions
Any vector, <a,b,c>, perpendicular to <3, -1, 1> must satisfy 3a-b+ c= 0
shouldnt there be a D value such that 3a-b+c+d=0
and how do i make sure they intersect
Homework Statement
For triangle XYZ, point P divides XZ in the ratio 3:1 and Q is the midpoint of XY. If R is the point of intersection of PY and QZ, find the ratio into which R divides PY.
Homework Equations
This is the only equation that may pertain to this that I can think of...
Homework Statement
Find an equation of the line through the point A (4,5,5) which meets the line (x-11)/3 = (y+8)/-1 = z-4 at right angles.
Homework Equations
The Attempt at a Solution
well i know that the direction of the given line is d(3,-1,1) and the original line crosses...