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Simplifying a(5i + -7j) + b(-7i + 2j) + (28i + 20j) = 0 (5i * a + -7j * a) + b(-7i + 2j) + (28i + 20j) = 0 (5ai + -7aj) + b(-7i + 2j) + (28i + 20j) = 0 5ai + -7aj + (-7i * b + 2j * b) + (28i + 20j) = 0 5ai + -7aj + (-7bi + 2bj) + (28i + 20j) = 0 Remove parenthesis around (28i + 20j) 5ai + -7aj + -7bi + 2bj + 28i + 20j = 0 Solving 5ai + -7aj + -7bi + 2bj + 28i + 20j = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '7bi' to each side of the equation. 5ai + -7aj + -7bi + 2bj + 28i + 7bi + 20j = 0 + 7bi Reorder the terms: 5ai + -7aj + -7bi + 7bi + 2bj + 28i + 20j = 0 + 7bi Combine like terms: -7bi + 7bi = 0 5ai + -7aj + 0 + 2bj + 28i + 20j = 0 + 7bi 5ai + -7aj + 2bj + 28i + 20j = 0 + 7bi Remove the zero: 5ai + -7aj + 2bj + 28i + 20j = 7bi Add '-2bj' to each side of the equation. 5ai + -7aj + 2bj + 28i + -2bj + 20j = 7bi + -2bj Reorder the terms: 5ai + -7aj + 2bj + -2bj + 28i + 20j = 7bi + -2bj Combine like terms: 2bj + -2bj = 0 5ai + -7aj + 0 + 28i + 20j = 7bi + -2bj 5ai + -7aj + 28i + 20j = 7bi + -2bj Add '-28i' to each side of the equation. 5ai + -7aj + 28i + -28i + 20j = 7bi + -2bj + -28i Combine like terms: 28i + -28i = 0 5ai + -7aj + 0 + 20j = 7bi + -2bj + -28i 5ai + -7aj + 20j = 7bi + -2bj + -28i Add '-20j' to each side of the equation. 5ai + -7aj + 20j + -20j = 7bi + -2bj + -28i + -20j Combine like terms: 20j + -20j = 0 5ai + -7aj + 0 = 7bi + -2bj + -28i + -20j 5ai + -7aj = 7bi + -2bj + -28i + -20j Reorder the terms: 5ai + -7aj + -7bi + 2bj + 28i + 20j = 7bi + -7bi + -2bj + 2bj + -28i + 28i + -20j + 20j Combine like terms: 7bi + -7bi = 0 5ai + -7aj + -7bi + 2bj + 28i + 20j = 0 + -2bj + 2bj + -28i + 28i + -20j + 20j 5ai + -7aj + -7bi + 2bj + 28i + 20j = -2bj + 2bj + -28i + 28i + -20j + 20j Combine like terms: -2bj + 2bj = 0 5ai + -7aj + -7bi + 2bj + 28i + 20j = 0 + -28i + 28i + -20j + 20j 5ai + -7aj + -7bi + 2bj + 28i + 20j = -28i + 28i + -20j + 20j Combine like terms: -28i + 28i = 0 5ai + -7aj + -7bi + 2bj + 28i + 20j = 0 + -20j + 20j 5ai + -7aj + -7bi + 2bj + 28i + 20j = -20j + 20j Combine like terms: -20j + 20j = 0 5ai + -7aj + -7bi + 2bj + 28i + 20j = 0 The solution to this equation could not be determined.
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