Homework # 5 - Math 250
The problems on this homework must be done alone. The honor code is in effect.
First name: Last name:
1. Find an equation of the plane through \((1, 0, 1)\) parallel to \(2x - 3y + 5z = 8\).
a. \(x - y - z = 0\)
b. \(4x + 2y - z = 3\)
c. \(2x - 3y + 5z = 4\)
d. \(4x - 6y + 10z = 14\)
e. \(z - y - z = -1\)
2. Find the intersection of the plane \(x + 2y - 3z = 10\) and the line given by \(x = 4+t\), \(y = 2t\), \(z= 2-t\)
a. \((7,3,1)\)
b. \((\frac{9}{2},1,\frac{3}{2})\)
c. \((\frac{11}{2},3,\frac{1}{2})\)
d. \((4,0,2)\)
e. They don't intersect.
3. Consider the line given by \(x = 3 - t\), \(y = -2 + 3t\), \(z = 2 + t\), and the line given by \(x = 1 + s\), \(y = 3 - s\), \(z = 2 + 3s\). Do these two lines intersect? If so, where do they intersect?
a. The lines don't intersect.
b. The lines intersect at \((-1, 3, 1)\).
c. The lines intersect at \((2, 1, 3)\).
d. The lines intersect at \((1.5, 2.5, 3.5)\)
e. The lines intersect at the origin.
4. Find the distance from the origin to the plane \(3x + 4y + 12z = 12\).
a. \(\frac{11}{13}\)
b. \(\frac{12}{13}\)
c. 1
d. \(\frac{14}{13}\)
e. \(\frac{15}{13}\)
5. Find the distance from the point (-1, 1, 2) to the line \(x = t\), \(y = 2t\), \(z = 2t\).
a. \(\frac{\sqrt{29}}{3}\)
b. \(\sqrt{29}\)
c. 2
d. \(\sqrt{3}\)
e. \(\frac{\sqrt{3}}{2}\)
6. In \(R^3\) what's does the following equation represent \(x^2 + 4y^2 = 4\)?
a. A sphere of radius 4 centered at the origin.
b. An elipse.
c. A hyperbola.
d. An eliptical cylinder centered on the x-axis.
e. An eliptical cylinder centered on the z-axis.