Question
In: Physics
Ax = 6m and Ay= -8m, Bx= -8m and By= 3m, Cx = 27m and Cy=...
Ax = 6m and Ay= -8m, Bx= -8m and By= 3m, Cx = 27m and Cy= 21m. Determine a and b such that aA + bB + C = 0. Include a sketch of the scenario.
Solutions
Expert Solution
aA = a * (Ax + Ay)
= a * (6 
- 8 
) ...(1)
bB = b * (Bx + By)
= b * (- 8
+ 3
) ...(2)
C = Cx + Cy
= 27
+ 21
...(3)
Adding (1) + (2) + (3) gives
aA + bB + C = a * (6
- 8
) + b * (- 8
+ 3
) + (27
+ 21
) = 0
(6 * a - 8 * b + 27)
+ (- 8 * a + 3 * b + 21)
= 0
Equating x-components,
6 * a - 8 * b + 27 = 0 ...(4)
Equating y-components,
- 8 * a + 3 * b + 21 = 0
- 8 * a = - 3 * b - 21
a = 1/8 * (3 * b + 21) ...(5)
Substituting a in (4),
6 * [1/8 * (3 * b + 21)] - 8 * b = - 27
2.25 * b + 15.75 - 8 * b = - 27
- 5.75 * b = - 42.75
b = 42.75 / 5.75
b = 7.43
Substituting b in (5),
a = 1/8 * [3 * 7.43 + 21]
= 43.30 / 8
a = 5.41
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