MATH 222 Midterm: MATH 222 KSU Test 1f99
15 Feb 2019
School
Department
Course
Professor
CALCULUS III NAME
EXAM I Rec. Instr.
FALL 1999 Rec. Time
TO RECEIVE CREDIT YOU MUST SHOW YOUR WORK.
(25) 1. Given the three points P(1,0,2) , Q(2,2,1) and R(0,1,4) , let ∆P QR
denote the triangle having P,Qand Ras vertices. Find
a) the area of ∆P QR .
b) the angle of ∆P QR at the vertex P.
c) the equation of the plane containing the points P,Qand R.
d) equations for the line through point Pwhich is perpendicular to the
plane containing ∆P QR .
1
NAME
Rec. Instr.
(10) 2. An object is moving around the ellipse x2+2y2= 100 in the xy-plane .
It is moving at a constant speed of 3 ft/sec. Specify whether each of the
following statements is true or false and explain why.
a) The acceleration vector is zero.
b) The velocity vector is zero.
c) At each instant the acceleration vector is perpendicular to the velocity
vector.
d) At each instant the acceleration vector is parallel to the velocity vector.
2
Document Summary
To receive credit you must show your work. (25) 1. Given the three points p (1, 0, 2) , q(2, 2, 1) and r(0, 1, 4) , let p qr denote the triangle having p , q and r as vertices. An object is moving around the ellipse x2+2y2 = 100 in the xy-plane . It is moving at a constant speed of 3 ft/sec. An object is moving in 3-space in such a way that its acceleration vector as a function of time is ~a = 2~j (sin t)~k . Suppose that at time t = 0 we know that ~v(0) = ~i + ~j and ~r(0) = ~i . Find the velocity vector and the position vector as functions of the time t and then give the parametric equations for the motion. An object is moving in 3-space according to the parametric equations x = sin t , y = cos t , z = sin 2t .
