In Fig. 3-31, a cube of edge length a 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, 0), (b) coordinates ( a , 0, 0), (c) coordinates (0, a , 0), and (d) coordinates ( a , a , 0)? (e) Determine the angles that the body diagonals make with the adjacent edges, (f) Determine the length of the body diagonals in terms of a . Figure 3-31 Problem 32.
In Fig. 3-31, a cube of edge length a 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, 0), (b) coordinates ( a , 0, 0), (c) coordinates (0, a , 0), and (d) coordinates ( a , a , 0)? (e) Determine the angles that the body diagonals make with the adjacent edges, (f) Determine the length of the body diagonals in terms of a . Figure 3-31 Problem 32.
In Fig. 3-31, a cube of edge length a 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, 0), (b) coordinates (a, 0, 0), (c) coordinates (0, a, 0), and (d) coordinates (a, a, 0)? (e) Determine the angles that the body diagonals make with the adjacent edges, (f) Determine the length of the body diagonals in terms of a.
Problem 8: Two vectors in Cartesian coordinates have components A = (1, 3, 2) and B = (4, 2, 5).
IAI =
Part (a) What is the length of the vector A?
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tanh()
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Part (b) What is the length of the vector B?
Part (c) What is the angle, in degrees, between A and B?
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Three Vectors A,B and C each having a magnitude of 50 units, lie in the XY and makes an angle of 30 degrees, 195 degrees and 315 degrees counter-clockwise from the positive x-axis, respectively. Find rhe magnitudes and the vectors: (a) A + B + C (b) (A-B) + C. Use close the polygon method.
Vectors A and B lie in an xy plane. A has magnitude 7.6 and angle 116° relative to +x direction: ☎ has components B, -4.14 and 8,
--3.53. What are the angles between the negative direction of the y axis and (a) the direction of A. (b) the direction of the product
Ax B, and (c) the direction of Ax (B+3.00A)?
(a) Number
154
(b) Number 90
(c) Number
150.3418858
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Units *(degrees)
Units "(degrees)
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