If vector A = (5.00 i -7.00 j) units, vector B = (-7.00 i + 2.00 j) units, and vector C = (25.0 i + 22.0 j) units, determine a and b such that a vector A + b vector B + vector C= 0.
a= ?
b=?
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2020-09-21 11:50 pm
回答 (1)
2020-09-22 12:21 am
a vectorA + b vector B + vector C = 0
a (5.00 i - 7.00 j) + b (-7.00 i + 2.00 j) + (25.0 i + 22.0 j) = 0
((5.00a - 7.00b + 25.0) i + (-7.00a + 2.00b + 22.0) j) = 0
The real part: 5.00a - 7.00b + 25.0 = 0 …... [1]
The imaginary part: -7.00a + 2.00b + 22.0 = 0 …… [2]
[1] × 7: 35.0a - 49.0b + 175 = 0 …… [3]
[2] × 5: -35.0a + 10.0b + 110 = 0 …… [4]
[3] + [4]:
-39.0b + 285 = 0
b = 7.31
Plug b = 7.31 into [1]:
5.00a - 7.00(7.31) + 25.0 = 0
a = 5.23
Hence, a = 5.23 and b = 7.31
a (5.00 i - 7.00 j) + b (-7.00 i + 2.00 j) + (25.0 i + 22.0 j) = 0
((5.00a - 7.00b + 25.0) i + (-7.00a + 2.00b + 22.0) j) = 0
The real part: 5.00a - 7.00b + 25.0 = 0 …... [1]
The imaginary part: -7.00a + 2.00b + 22.0 = 0 …… [2]
[1] × 7: 35.0a - 49.0b + 175 = 0 …… [3]
[2] × 5: -35.0a + 10.0b + 110 = 0 …… [4]
[3] + [4]:
-39.0b + 285 = 0
b = 7.31
Plug b = 7.31 into [1]:
5.00a - 7.00(7.31) + 25.0 = 0
a = 5.23
Hence, a = 5.23 and b = 7.31
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