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Unknown components that make two vectors collinear

This type of question, asked 3 times: 17 Apr 2026 S2, 13 May 2026 S2, 14 May 2026 S1. All 3 questions below, oldest first.

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  1. Question 1

    17 Apr 2026 S2

    91
    Let a⃗=λi^+j^+k^,b⃗=2i^+4j^+4k^,c⃗=i^+μj^+k^\vec{a} = \lambda\hat{i} + \hat{j} + \hat{k}, \vec{b} = 2\hat{i} + 4\hat{j} + 4\hat{k}, \vec{c} = \hat{i} + \mu\hat{j} + \hat{k} If a⃗\vec{a} is parallel to b⃗\vec{b} and b⃗\vec{b} is perpendicular to c⃗\vec{c} then λ−μ=…\lambda - \mu = \ldots

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  2. Question 2

    13 May 2026 S2

    90
    If the vector a⃗=xi^−j^+k^\vec{a} = x\hat{i} - \hat{j} + \hat{k} and b⃗=i^+yj^+zk^\vec{b} = \hat{i} + y\hat{j} + z\hat{k} are collinear, then a possible unit vector parallel to the vector i^+yj^+zk^\hat{i} + y\hat{j} + z\hat{k} is...

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  3. Question 3

    14 May 2026 S1

    91
    If aˉ=4i^−10j^+(1−p)k^\bar{a} = 4\hat{i} - 10\hat{j} + (1 - p)\hat{k} and bˉ=12i^+(q−10)j^+3k^\bar{b} = 12\hat{i} + (q - 10)\hat{j} + 3\hat{k} satisfy aˉ×bˉ=0ˉ\bar{a} \times \bar{b} = \bar{0}, then the values of pp and qq are respectively

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