MATH 599 Midterm: MATH 5B UCSB 5B Fall 06 5BpMidterm s1
Document Summary
Math 5b, midterm 1 review problems - solutions. The vector v = n1 n2 is orthogonal to both n1 and n2 by de nition, and so it is parallel to both planes. That is, v is the direction vector of the line that we want. v = (2, 1, 1) ( 1, 1, 1) = (cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12) i j. To get a point on the line, we can set z = 0 in the two equations of the planes and solve the resulting system of two equations for x and y. Solving for x and y yields x = 4 and y = 7, so (4, 7, 0) is a point on both planes, and thus on their line of intersection. If there were such a line, its direction vector would be normal to both planes. Since (1, 1, 1) must be in the plane, we get the equation. = 7i + 2j + 4k = ( 7, 2, 4).
