Section Practice
¶These are practice problems for the tests. Solutions are in the next section. While we will not present these, I am happy to answer questions about them in class.
Cross Products
Compute the cross product of \(\oa u = (3,2,-1)\) and \(\oa v = (2,\pi,-3)\) and state the significance of the resulting vector.
Find two vectors of unit length orthogonal to both \(\oa a = (4,-3,2)\) and \(\oa b = (2,5,-3).\)
Planes
Find the equation of a plane parallel to \(3x +2z = 4 - y\) and containing \((2,4,-2).\)
Find the equation of the line that represents the intersection of \(3z - 4x + 2y = 4\) and \(2z - x = 6 - y.\)
Find an equation for the plane containing \((1,2,3), (2,3,4),\) and \((-1,1,1).\) Find another equation for the same plane.
Find the distance between the two planes: \(2x-3y+5z=5\) and \(2x-3y+5z=15\text{.}\)