{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Practice_Exam1_v_2

# Practice_Exam1_v_2 - c3 18.02 Practice Exam 1A{50 mins...

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: c3 18.02)! Practice Exam 1A {50 mins.) ProbIEm l (25 pts: 5, 10, 10) The rectangular _box has edges of lengths 1,2,3 lying aiong the coordinate axes, as shown. Using head—to—tail addition, R0 = -2i + k. _ € 5.) Express similarly PO and PR in terms of i, j. and k . b) Find the cosine of the angle 6 = RPQ. c) Find a perpendicular vector to the plane through P, Q, and R, and find the area of triangle PQR. Problem 2. (25 pts: 10. 1o, 51 ,_ 1 0 '1 . . . . - 41/2 1 —1/2 a) If A = 2 l 2 ’ 31111 :ntthesmilslsing A-1 = _2 1 2 73 I" 1‘ IE - 3/2 b) Solve x1 + Ik3 = 2 if C = 3. using part (a). 2x1 + x2 +‘2x3 = 1 x1 + 2x2 + cx3 = 3 Then check the value'of _x by using Cramer’s ruler' {Show work.) 1 c) For one value of c the system in (b) has'no sclution. .Find this 'vaiue. Problem 3. (25 pts.: 5, 10, 10) _ A moVing point P has coordinates -x =. (t - 112. y =, t2. 2 = 2t - 1. ‘ a) Where (i.e., a_t what point) does it pass through the yz-plane? b) At time t = 0, find its speed and the unit tangent vector to the motion.- c) Find a constant vector perpendicular to the position vector R a 0?. What does this tell you geometrically about the motion? ' Problem 4. (10 pts.) Scotch tape is being peeled off a roll of radius a. starting at the point A. The end -P:(x,y) is always'puiied vertically upwards. Use vector methods to write parametric equations for x and y terms of 6, for Q s 9 s 1: (see ﬁg. helm.) Problem 5. (10 pts.) Using. the standard operations on vectors. prove that if the diagonals of a parallelogram are perpendicular. its four sides have equal length. Problem 6. (5 pts). A point moves with constant speed. Prove its velocity vector v and itsacceleration vector a are always perpendicular. (Consider v-v .) P 0. H 9:2; ADG’ ...
View Full Document

{[ snackBarMessage ]}