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a = j - k, c = i - j - k: vector b with a x b + c = 0 and a.b = 3

The same question, asked 2 times: 3 May 2023 S2, 10 May 2023 S2. Every wording below, oldest first.

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  1. Question 1

    3 May 2023 S2

    133
    Let a⃗=j^−k^\vec{a}=\hat{j}-\hat{k} and c⃗=i^−j^−k^\vec{c}=\hat{i}-\hat{j}-\hat{k}. Then the vector b⃗\vec{b} satisfying a⃗×b⃗+c⃗=0⃗\vec{a}\times\vec{b}+\vec{c}=\vec{0} and a⃗⋅b⃗=3\vec{a}\cdot\vec{b}=3, is

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  2. Question 2

    10 May 2023 S2

    117
    If a⃗=j^−k^\vec{a} = \hat{j}-\hat{k} and c⃗=i^−j^−k^\vec{c} = \hat{i}-\hat{j}-\hat{k}, then the vector b⃗\vec{b} satisfying a⃗×b⃗+c⃗=0⃗\vec{a}\times\vec{b}+\vec{c}=\vec{0} and a⃗⋅b⃗=3\vec{a}\cdot\vec{b}=3 is

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