1. The magnitude of F above is 100 lb. It makes a 60 degree angle with the x-axi
ID: 1956980 • Letter: 1
Question
1.The magnitude of F above is 100 lb. It makes a 60 degree angle with the x-axis. The magnitude of the vector r from the origin to point A is 8ft.2.
-Use the definition of the dot product to determine r dot F
-Use a matrix to find the dot product
The coordinates for point A are (4,3,2), those of point C are (8,8,4), and those of point B are (6,1,-2). Find the angle between AC and AB.
3.
Resolve the force along its x and y axis and write in vector form.
Is the answer simply Vector F = 80N sin 30 - 80N cos 30?
Explanation / Answer
1)r= 8ft (i) F = 100cos60 (i) +100 sin60 (j) = 50 (i) + 86.6 (j) r.F = 800 lb-ft 2)A(4,3,2) ; B(6,1,-2) ; C(8,8,4) angle between AB and AC AB =(6,1,-2)-(4,3,2) =(2,-2,-4) |AB| =sqrt(4+4+16) =4.89 AC =(8,8,4)-(4,3,2) = (4,5,2) |AC| = sqrt(16+25+4) =6.70 cos (?) =AB.AC/|AB|*|AC| = [(2*4)+ (-2*5)+(-4*2)]/4.89*6.7 ? =72.2 degrees 3)YES it is correct F=80sin30 i - 80cos30 j
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