I need help with these questions.....they're from grade 12 geometry and discrete math.
1. Analyse the normal vectors of the following planes and describe the situation of each system. Include a geometric interpretation of each solution:
7x-5y+4z-9=0
-5x+4y+z-3=0
x+2y-z+1=0
2. Analyse the normal vectors of the following planes and describe the situation of each system. Include a geometric interpretation of each solution:
7x-5y+4z-9=0
-x+3y+5z-2=0
5x+y+14z-20=0
3. Determine the parametric equations for a line that is perpendicular to the
yz-plane and passes through X(-2,4,3).
4. If a line and its normal vector with tail at (0,0) intersect at N(-2,5), determine the equation of the line.
5. A line has a scalar equation 5x+2y-10=0. Express the equation of the line in symmetric form.
6. Explain how knowing the normal vectors of two non-parallel planes can be
used to determine the scalar equation of another plane that is perpendicular to the two given planes.
7. Determine whether the two lines intersect and, if so, determine the
point(s) of intersection.
Hello,
Let L be the name of the line. Then:
1.
2. The normal vector of the line is:
If is the position vector of every point of the line and is the position vector to a fixed point A on the line then
Use this equation:
Expand and you'll get: -2x + 5y -29 = 0 <-- equation of the line
Hello,
I don't know a "symmetric form" of an equation. If you are looking for an equation of the line using vectors you calculate first the coordinates of 2 points which represent the position vectors of thesepoints:
A(2, 0)
B(0, 5)
The direction vector of the line is:
Now you have the fixed point A and the direction of the line. Therefore the equation is: