D1.7. Given the two points, C(-3, 2, 1) and D(r 5, 0 20, = - 70), find: (a) the spherical coordinates of C; (b) the rectangular coordinates of D: (c) the distance from C to D.
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- The functions ¢1(x) and ø2(x) are normalized: d φ( (α) φι(α) dx 0(x) 62(x) = 1 = 1 -00 -00 and are mutually orthogonal dx oi(x) $2(x) dx 4i(x) $1(x) = 0 . Is the function b_(x) = ¢1(x) – $2(x) normalized? If not, determine its normalization constant and write the formula for the normalized y_ (x). Is the function +(x) = ¢1(x) + ¢2(x) %3D orthogonal to _(x)?1-9. For the two vectors A = i + 2j – k, B = -2i + 3j + k find (a) A – B and |A – B| (b) component of B along A (d) A X B (c) angle between A and B (e) (A – B) × (A + B)Say that a is a vector (nonzero) in the third dimension. b and c are two other vectors. If a • b = a • c, and a x b = a x c, is b = c?
- After enjoying a big sandwich at Katz's Delicatessen, you decide to walk back to your luxury suite at the Waldorf-Astoria Hotel. First, you perambulate 0.15 mi at a polar angle of 160 degrees 0.15 mi angle 160^ ) . Next, you skedaddle 1.60 mi at a polar angle of 55 degrees (1.60 mi angle55^ ) . You follow this with a 0.55 mi jaunt at a polar angle of 150 degrees (0.55 mi angle150^ ) Finally, you be-bop 0.82 mi at a polar angle of 60 degrees (0.82 mi angle 60^ ) . What is the overall displacement from your starting point at Katz's Delicatessen? Express your answer in polar notation.What is the angle θDθDformed by D⃗ (from the picture) and the +x+xaxis? Use counterclockwise to denote positive angles. Answer with 2 significant figures.1. ANALYTICAL METHOD OF ADDING VECTORS Solve the same problem as PART 1 but this time analytically. START with the values below. DO NOT USE VALUES FROM PART 1. Suppose you first walk A = 12 m in a direction 20° west of north and then B= 20 m in a direction 40° south of west. Let the +x-axis coincide with the easterly direction and the +y-axis with the northerly direction. Note: In this problem, do not round values if you need to use them for calculations in subsequent parts. Rounding errors can propagate and can make your final answer lie outside the tolerance limit of 5% set for this problem. Keep all answers to 4 significant figures.
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