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Angle between two vectors given in component form

This type of question, asked 2 times: 20 Apr 2025 S1, 16 Apr 2026 S1. All 2 questions below, oldest first.

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  1. Question 1

    20 Apr 2025 S1

    16
    If A→=i^+j^+3k^,B→=−i^+j^+4k^\overrightarrow{A}=\widehat{i}+\widehat{j}+ 3\widehat{k},\overrightarrow{B}= -\widehat{i}+\widehat{j}+ 4\widehat{k} and C→=2i^−2j^−8k^\overrightarrow{C}= 2\widehat{i}- 2\widehat{j}- 8\widehat{k}, then the angle between the vectors P→=A→+B→+C→\overrightarrow{P}=\overrightarrow{A}+\overrightarrow{B}+\overrightarrow{C} and Q→=(A→×B→)\overrightarrow{Q}= (\overrightarrow{A}\times\overrightarrow{B}) is (in degree)

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  2. Question 2

    16 Apr 2026 S1

    102
    Let P⃗=i^+j^+k^\vec{P} = \hat{i} + \hat{j} + \hat{k} and Q⃗=−(i^+j^+k^)\vec{Q} = -(\hat{i} + \hat{j} + \hat{k}). The angle between (P⃗−Q⃗)(\vec{P} - \vec{Q}) and P⃗\vec{P} is

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