MATH-4600
J. W. Banks
Due: Monday January 13, 2025
Problem Set 1
Submissions are due in the LMS by the end of the day.
1. Given two vectors vand w.
(a) Determine vk(component of vparallel to w) and v⊥(component of vperpendicular to
w).
(b) What is the area of the triangle with sides vand w?
For this problem you may find it useful to draw a sketch.
2. Suppose the 3 points A= (a1, a2, a3),B= (b1, b2, b3), and C= (c1, c2, c3)in R3are given.
(a) Determine an equation for the plane defined by A,B, and C, as well as an equation for
its normal.
(b) Determine an equation for the the area of the triangle with vertices A,B, and Cassuming
a3=b3=c3= 0.
3. Consider surfaces S1defined by sin2(x)ecos(y)+z3= 2, and S2defined by x2+y2= 1.
(a) Determine an equation for the tangent plane to S1at the point (π
2,π
2,1).
(b) Determine an equation for the intersection of S2and the tangent plane determined in
part (a) above.
Suggested Problems form Colley
1. Section 1.1: 1, 3, 5, 15, 21, 27
2. Section 1.2: 1, 3, 5, 7, 9, 11, 13, 17, 21, 23, 25, 33, 35, 45
3. Section 1.3: 1, 3, 5, 7, 9, 11, 13, 15, 17, 21, 25, 27, 33
4. Section 1.4: 1, 3, 5, 7, 9, 11, 17, 19, 25, 37
5. Section 1.5: 1, 3, 5, 9, 11, 13, 17, 21, 23, 25, 27, 31
6. Section 1.7: 1, 3, 5, 7, 11, 15, 17, 19, 21, 23, 27, 31
1