Unformatted text preview: Problem 6. 10 points M4080 Exam 3 Sato Problem 1. Spointseach. Let A = 3i + 2j - k, B=<-1,0,—‘l >. C: <O,1,0>
a. Find 3A-B
b. Ftnd (AxC)o2A
c. Find (A—B):(A+B)
d. Find (B-—C) x 3
Problem 2. to points The two planes given by the equations 2): — y + z = 5 and (x — 2) + 2(y — 1) + (z + 5) = 0
intersect in a line. Find either vector or scalar parametric equations for that line. Problem 3. 5 points each.
Let fix, y) = sinixy)! (x2+y2).
a. Find lim f(x. y) as (x, y) approaches (0,0) along the x—axis.
(x. 9-4013) b. Find tim f(x. y) as (x, y) approaches (0, 0) along the line y = x. What does
(2:. y) H (0.0)
this tell you about whether the whole limit exists?
Problem 4. Two planes are given by the equations 2x - y + z = 2 and 2(x-1) - (y+t) + (2—3) = O.
a. 5 points. Show that they are parallel. Give a speciﬁc reason for your answer.
b. 10 points. Find the distance between the two planes. Problem 5. 10 points The curves R16) = <1 t2, t3, t4 > and R2(s) = < e‘, cos 5, 1 + ln(1+s) > both pass through the
point (t, 1. 1.). Find an equation for the plane passing through this point containing both tangent
lines to the curvesat’this point. if you have difﬁculty with this, partial credit wiii be given for finding egsations. ratiﬁes tansspt_li_nse Find the area of the shaded region: r=1+sine Problem 1. 10 points Find the center and radius of the circle given. by r= cos a + 2 sin e. Probtem 8. 10 points. A curve in 3—dimensionat space is given by Re) e < sin t, t3.
through the point (0. 0, -1). Write symmetric equations for the tangent line to the curve at that point. Partial credit will be given for parametric equations and finding a tangent vector. —cos t 2- passes ...
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- Spring '07