- #1
DOH-WLcat
- 5
- 0
1. Find the volume, using triple integrals, of the region in the first octant beneath the plane 2x+3y+2z = 6
2. http://tutorial.math.lamar.edu/Classes/CalcIII/TripleIntegrals.aspx
SOLUTION:
1. Assume X and Y are 0. Solve for Z: 2(0)+3(0)+2z=6 => z=3 (0,0,3)
2. Assume X and Z are 0. Solve for Y: 2(0)+3(y)+2(0)=6 => y=2 (0,2,0)
3. Assume Y and Z are 0. Solve for X: 2(x)+3(0)+2(0)=6 => x=3 (3,0,0)
4. The plane in question passes through three points: (0,0,3), (0,2,0), (3,0,0). Find two vectors parallel to this plane.
a. V = (3,0,0) - (0,2,0) = (3,-2,0)
b. W = (3,0,0) - (0,0,3) = (3,0,-3)
5. Compute a Normal vector N of this plane with the two vectors obtained in the previous two steps.
a. N = v*w = (3,-2,0) [(3,0,-3)]
b. i.=6, j.= - 9 and k.=6
c. (6x-9y+6z) = ((x-3)i+yj+zk) => 6x-9y+6z=18 => Solve for Z: z= -x+3y/2+3
d. Solve for y => (using the slope equation: (0-2)/(3-0)=> -2x/3+2 =y
e. Solve for X => We already know that it is 3.
f. Plug in x, y, and z information into the formula listed above.
e. My answer is 9, but the [final exam review for this problem is 3]
Please help. I am taking my final this week to finish my summer school before school starts next week.
Thank you all for your help.
DOH-WLcat.
2. http://tutorial.math.lamar.edu/Classes/CalcIII/TripleIntegrals.aspx
SOLUTION:
1. Assume X and Y are 0. Solve for Z: 2(0)+3(0)+2z=6 => z=3 (0,0,3)
2. Assume X and Z are 0. Solve for Y: 2(0)+3(y)+2(0)=6 => y=2 (0,2,0)
3. Assume Y and Z are 0. Solve for X: 2(x)+3(0)+2(0)=6 => x=3 (3,0,0)
4. The plane in question passes through three points: (0,0,3), (0,2,0), (3,0,0). Find two vectors parallel to this plane.
a. V = (3,0,0) - (0,2,0) = (3,-2,0)
b. W = (3,0,0) - (0,0,3) = (3,0,-3)
5. Compute a Normal vector N of this plane with the two vectors obtained in the previous two steps.
a. N = v*w = (3,-2,0) [(3,0,-3)]
b. i.=6, j.= - 9 and k.=6
c. (6x-9y+6z) = ((x-3)i+yj+zk) => 6x-9y+6z=18 => Solve for Z: z= -x+3y/2+3
d. Solve for y => (using the slope equation: (0-2)/(3-0)=> -2x/3+2 =y
e. Solve for X => We already know that it is 3.
f. Plug in x, y, and z information into the formula listed above.
e. My answer is 9, but the [final exam review for this problem is 3]
Please help. I am taking my final this week to finish my summer school before school starts next week.
Thank you all for your help.
DOH-WLcat.