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Write a vector as a combination of given vectors

This type of question, asked 2 times: 10 May 2024 S2, 15 May 2026 S2. All 2 questions below, oldest first.

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  1. Question 1

    10 May 2024 S2

    136
    If a⃗=mb⃗+nc⃗\vec{a}=m\vec{b}+n\vec{c}, where a⃗=4i^+13j^−18k^\vec{a}=4\hat{i}+13\hat{j}-18\hat{k}, b⃗=i^−2j^+3k^\vec{b}=\hat{i}-2\hat{j}+3\hat{k}, c⃗=2i^+3j^−4k^\vec{c}=2\hat{i}+3\hat{j}-4\hat{k}, then m+n=m+n=

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  2. Question 2

    15 May 2026 S2

    89
    If aˉ=2i^−j^+k^\bar{a} = 2\hat{i} - \hat{j} + \hat{k}, bˉ=i^+3j^−k^\bar{b} = \hat{i} + 3\hat{j} - \hat{k}, cˉ=−2i^+j^−3k^\bar{c} = -2\hat{i} + \hat{j} - 3\hat{k} and dˉ=3i^+2j^+5k^\bar{d} = 3\hat{i} + 2\hat{j} + 5\hat{k}, then the value of x2+z2−yx^2 + z^2 - y is ⋯\cdots, where dˉ=xaˉ+ybˉ+zcˉ\bar{d} = x\bar{a} + y\bar{b} + z\bar{c}

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