5.- For A = 3î +ĵ-k, B = −î+ 2ĵ+ 5k and C = 2j - 3k, find a) C - (Ā – B), b) (Ā + C)xB

A.) i. Define the plane polar unit vectors ŕ and 0 and show that they are orthonormal. Determine dr dê and de de ii. Hence show that for the vector r(t) = r(t)ŕ dr · = rî +rðê, d²r and = - dt dt² († − rė²)ŕ + (2ŕė +rë)ê . iii. If a mass m moves in the plane along r(t) = a and (t) = 5t determine the shape of the motion and find its period. B) Show that the motion of an object under the universal gravitational force μη Fg is governed by the radial and angular equations of motion and μ = 0, 2r0+ rö = 0. Setting r(t) =R for some constant R, solve these equations of motion and determine the period of the motion. C) Consider the following non-linear differential equation *+5= x +4. Find the stationary solutions. Expand around each of the stationary so- lutions that you have found, in order to determine if they correspond to stable or unstable equilibria. D) Show that 1 5 E = 2 - 4x is a conserved quantity. Hence draw the phase-space diagram and de- termine for which values of E oscilations…

2) Express the speed of light, 3.00 × 108 m/s, in (a) ft/ns; (b) miles/s; (c) AU/h. I need to show all work

Force on q, by q, = 79.889N Force on q, by q, = 79.889N 91 O cm 3 4 5 7 8 10 Charge 1 Charge 2 Force Values -4 μC 2 μ Scientific Notation -10 10 -10 10 1 cm

S Can 6 PAR к Торс K Unit K In x K Moti = Cop K Unit S Spee S Topo S Math Micr eb.kamihq.com/web/viewer.html?source-filepicker&document_identifier=137VZR5BZOVSAIMOA55WU555_CvJ9NacO + 100 P e Interpreting Graphs Answer the questions following the graphs on each side Dietance va. Time 2 7 10 11 12 13 14 Time in soconds 1. From 1 second to 2 seconds, how fast is the object traveling. (Take the difference in distance and divide it by the time in between the 2 distances) 2. Is the object going as fast between 9 and 12 seconds as it is between 1 and 4 seconds? How can you tell? 3. What is the motion of the object between 4 and 6 seconds? acer

) if A = = 3i+4j +2K and B= -2i +6j +5k find A. B. (A .B änjö ) جد قيمة • B

K conditions 2 is 2.00 and K condition 1 is 1.88. Why should K condition 1 and 2 should be the same?

If =- 3;-63+ 1kand č= - 33 - 23- 3g, what is the magnitude of č x B (give your answer to the nearest 0.1)?

3. Let a, b, n be integers, with n > 0. Prove that a = b (mod n) if and only if a² + b² = 2ab (mod n²).

2- if à = 3i – j - 4k, B = -2i + 4j – 3k, Č = i + 2j – k, D = ai – 3j – 3k find : (a) 2à – B + 30 (b) JÄ + B + č| (c) Ả × B (d) B · Č (e) Ả · B × ở (f) Ả × (B x č) (8) (Ả x B) × ở %3D | (h) angle between Å · C (i) value of 1 that makes the vectors D· C orthogonal. (i) The area of a parallelogram that B · C are Two adjacent sides on it. (k) value of 1 that makes the vectors D· A orthogonal. (h) the component of A in direction of B.