If A = (6i-8j) units, B = (-8i-3j) units, and C = (26i-19j) units, determine a and b
such that aA + bB + C = 0 (
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Answer:
aA+bB+c = 0 then a =? b= ?
assuming that is the vector sum has to be zero...
x,y components have to add to zero
x:
a(6) + b(8) + 26 = 0
y:
a(–8) + b(3) + 19 = 0
two equations, 2 unknowns
6a + 8b + 26 = 0
–8a + 3b + 19 = 0
3a + 4b + 13 = 0
–8a + 3b + 19 = 0
multiply first by 3 and second by –4 and add
9a + 12b + 39 = 0
32a – 12b – 76 = 0
41a – 37 = 0
a = 37/41
6a + 8b + 26 = 0
6(37/41) + 8b + 26 = 0
8b = –26 – (222/41) = –1288/41
b = –161/41
check
6a + 8b + 26 = 0
–8a + 3b + 19 = 0
6(37/41) + 8(–161/41) + 26 = 0
–8(37/41) + 3(–161/41) + 19 = 0
222 – 1288 + 1066 = 0 ok
–296 – 483 + 779 = 0 ok
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