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Given |a|, |b| and |a x b|, find a . b (or its square)

The same question, asked 2 times: 2021 Paper 15*, 31 Jan 2023. Every wording below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    2021 Paper 15

    49
    If ∣a→∣=2,∣b→∣=5,∣a→×b→∣=8|\overrightarrow{a}| = 2,|\overrightarrow{b}| = 5,|\overrightarrow{a}\times\overrightarrow{b}| = 8, then ∣a→⋅b→∣=|\overrightarrow{a}\cdot\overrightarrow{b}| = ?

  2. Question 2

    31 Jan 2023

    87
    Let a→\overrightarrow{a} and b→\overrightarrow{b} be two vectors such that ∣a→∣=14,∣b→∣=6|\overrightarrow{a}| =\sqrt{14},|\overrightarrow{b}| =\sqrt{6} and ∣a→×b→∣=48|\overrightarrow{a}\times\overrightarrow{b}| =\sqrt{48}. Then (a→⋅b→)2(\overrightarrow{a}\cdot\overrightarrow{b})^{2} is equal to