Return to Blackboard alliday, Fundamentals of Physics, 10e PRINTER VERSION ·BACK

Question

Return to Blackboard alliday, Fundamentals of Physics, 10e PRINTER VERSION ·BACK In the figure, a cube of edge length a 3.40 m sits with one corner at the origin of an xyz coordinate system. A body diagonal is a line that extends from one corner to another through the center. In unit-vector notation, what is the body diagonal that extends from the corner at (a) coordinates (0, 0, O), (b) coordinates (a, O, O), () coordinates (o, a, 0), and (d) coordinates (o, , 0)? (e) Determine the angles that the body diagonals make with the adjacent edges. () Determine the length of the body ciagonals k units (a) Number k units (b) Number k Units (c) Number

Explanation / Answer

(A) |a| = sqrt(2^2 + (-1.50)^2) = 2.5

(B) theta = 360 - tan^-1(1.50/2) = 143 deg

(C) |b| = sqrt(3^2 + 4^2) = 5

(d) theta = tan^-1(4/3) = 53 deg

(e) a + b = (2 + 3)i + (-1.5 + 4)j = 5i + 2.5 j

magnitude = 5.6

(F) theta = tan^-1(2.5/5) = 26.6 deg

(g) b - a = i + 5.50 j

magnitude = 5.6

(h) theta = tan^-1(5.50/1) = 79.7 deg  

(i) a - b = - i - 5.50 j

magnitude = 5.6

(j) theta = 180 + 79.7 = 259.7 deg

(k) using dot product

(b - a).(a - b) = | b - a| |a - b| cos(theta)

(-1 x 1) + (-5.50^2) = (5.6 x 5.6) cos(theta)

theta = 175.2 deg

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