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Simplifying (-4i + -10j + k) + -1(6i + 10j + 6k) = 0 Remove parenthesis around (-4i + -10j + k) -4i + -10j + k + -1(6i + 10j + 6k) = 0 -4i + -10j + k + (6i * -1 + 10j * -1 + 6k * -1) = 0 -4i + -10j + k + (-6i + -10j + -6k) = 0 Reorder the terms: -4i + -6i + -10j + -10j + k + -6k = 0 Combine like terms: -4i + -6i = -10i -10i + -10j + -10j + k + -6k = 0 Combine like terms: -10j + -10j = -20j -10i + -20j + k + -6k = 0 Combine like terms: k + -6k = -5k -10i + -20j + -5k = 0 Solving -10i + -20j + -5k = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '20j' to each side of the equation. -10i + -20j + 20j + -5k = 0 + 20j Combine like terms: -20j + 20j = 0 -10i + 0 + -5k = 0 + 20j -10i + -5k = 0 + 20j Remove the zero: -10i + -5k = 20j Add '5k' to each side of the equation. -10i + -5k + 5k = 20j + 5k Combine like terms: -5k + 5k = 0 -10i + 0 = 20j + 5k -10i = 20j + 5k Divide each side by '-10'. i = -2j + -0.5k Simplifying i = -2j + -0.5k
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