MATH V1201 Midterm: Math V1201 Columbia Exam Solution

• School: Columbia University
• Department: Mathematics
• Course: MATH V1201
• Professor: All

Document Summary

Calculus iii practice questions: find the equation of the plane through the points (3, 1, 1), (4, 2, 0) and (6, 2, 1). Solution: by subtracting the rst point from the two subsequent points, we see that the following vectors lie on the plane: Take their cross product v1 = h1, 3, 1i, v2 = h3, 1, 0i. Therefore the plane has equation v1 v2 = h 1, 3, 10i. where d is to be determined. We substitute the point (4, 2, 0) to identify d: Therefore an equation for the plane is d = 4 3(2) 10(0) = 10. X 3y 10z = 10: find the values of x such that the vectors h3, 2, xi and h2x, 4, xi are orthogonal. Solution: take the dot product and set it equal to zero: 0 = h3, 2, xi h2x, 4, xi = 6x + 8 + x2 = (x + 2)(x + 4).