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Vector (unit or of given length) perpendicular to two given vectors

This type of question, asked 4 times: 10 May 2023 S2, 11 May 2023 S2, 11 May 2024 S2, 26 Apr 2025 S2. All 4 questions below, oldest first.

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  1. Question 1

    10 May 2023 S2

    112
    The vector of magnitude 6 units and perpendicular to vectors 2i^+j^−3k^2\hat{i}+\hat{j}-3\hat{k} and i^−2j^+k^\hat{i}-2\hat{j}+\hat{k} is

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  2. Question 2

    11 May 2023 S2

    134
    The number of unit vectors perpendicular to a⃗=(1,1,0)\vec{a}=(1,1,0) and b⃗=(0,1,1)\vec{b}=(0,1,1) is

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  3. Question 3

    11 May 2024 S2

    150
    The unit vector perpendicular to each of the vectors a⃗+b⃗\vec{a}+\vec{b} and a⃗−b⃗\vec{a}-\vec{b}, where a⃗=i^+j^+k^\vec{a}=\hat{i}+\hat{j}+\hat{k} and b⃗=3i^−2j^+5k^\vec{b}=3\hat{i}-2\hat{j}+5\hat{k} is:

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  4. Question 4

    26 Apr 2025 S2

    144
    The unit vectors perpendicular to the plane determined by the points A(1,−1,2),B(2,0,−1)A(1, - 1,2),B(2,0, - 1), C(0,2,1)C(0,2,1) is

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