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Let A→ = (150iˆ+270jˆ) mm, B→ = (300iˆ-450jˆ) mm, and C→ = (-100iˆ-250jˆ) mm. Find scalars r and s, if possible, such that R→=rA→+sB→+C→ has zero x and y components.

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  1. 31 March, 10:24
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    Answer: r = 0.8081; s = - 0.07071

    Explanation:

    A = (150i + 270j) mm

    B = (300i - 450j) mm

    C = (-100i - 250j) mm

    R = rA + sB + C = 0i + 0j

    R = r (150i + 270j) + s (300i - 450j) + (-100i - 250j) = 0i + 0j

    R = (150r + 300s - 100) i + (270r - 450s - 250) j = 0i + 0j

    Equating the i and j components;

    150r + 300s - 100 = 0

    270r - 450s - 250 = 0

    150r + 300s = 100

    270r - 450s = 250

    solving simultaneously,

    r = 0.8081 and s = - 0.07071

    QED!
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