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Dot or cross product from the magnitudes and the angle between vectors

This type of question, asked 3 times: 25 Apr 2025 S1, 26 Apr 2025 S1, 19 May 2026 S2. All 3 questions below, oldest first.

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  1. Question 1

    25 Apr 2025 S1

    10
    Vector A→\overrightarrow{A} of magnitude 535\sqrt{3} units, another vector B→\overrightarrow{B} of magnitude of 10 units are inclined to each other at an angle of 30∘30^{\circ}. The magnitude of vector product of the two vectors is [sin⁡30∘=12]\left\lbrack \sin30^{\circ}=\frac{1}{2} \right\rbrack

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  2. Question 2

    26 Apr 2025 S1

    11
    If ∣a→∣=26,∣b→∣=7|\overrightarrow{a}| =\sqrt{26},|\overrightarrow{b}| = 7 ∣a→×b→∣=35|\overrightarrow{a}\times\overrightarrow{b}| = 35, find a→⋅b→\overrightarrow{a}\cdot\overrightarrow{b}

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  3. Question 3

    19 May 2026 S2

    101
    A vector A⃗\vec{A} of magnitude 727\sqrt{2} unit, another vector B⃗\vec{B} of magnitude 1414 unit are inclined at an angle of 60∘60^\circ. The magnitude of the scalar product (A⃗⋅B⃗)(\vec{A} \cdot \vec{B}) is [cos⁡(60)∘=12]\left[\cos(60)^\circ = \dfrac{1}{2}\right]

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