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Resultant or unit vector of vectors given in component form

This type of question, asked 3 times: 20 Apr 2025 S2, 21 Apr 2025 S2, 15 Apr 2026 S1. All 3 questions below, oldest first.

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  1. Question 1

    20 Apr 2025 S2

    7
    Three vectors are expressed as a→=4i^−j^,b→=−3i^+2j^\overrightarrow{a}= 4\widehat{i}-\widehat{j},\overrightarrow{b}= - 3\widehat{i}+ 2\widehat{j} and c→=−k^\overrightarrow{c}= -\widehat{k}. The unit vector along the direction of sum of these vectors is

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  2. Question 2

    21 Apr 2025 S2

    3
    A unit vector in the direction of resultant vector of A→=−2i^+3j^+k^\overrightarrow{A}= - 2\widehat{i}+ 3\widehat{j}+\widehat{k} and B→=i^+2j^−4k^\overrightarrow{B}=\widehat{i}+ 2\widehat{j}- 4\widehat{k} is

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  3. Question 3

    15 Apr 2026 S1

    102
    A vector A⃗\vec{A} when added to the sum of the vectors (i^−2j^+2k^)(\hat{i} - 2\hat{j} + 2\hat{k}) and (−2i^+j^−k^)(-2\hat{i} + \hat{j} - \hat{k}) gives a unit vector along Y axis. The magnitude of vector A⃗\vec{A} is

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