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|b x c| from the volume of a tetrahedron and the projection or angle of a on b x c

This type of question, asked 2 times: 19 Apr 2025 S1, 13 May 2026 S1. All 2 questions below, oldest first.

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  1. Question 1

    19 Apr 2025 S1

    127
    The volume of the tetrahedron whose co-terminus edges are aˉ,bˉ,cˉ\bar{a},\bar{b},\bar{c} is 12 cubic units. If the scalar projection of aˉ\bar{a} on bˉ×cˉ\bar{b}\times\bar{c} is 4, then ∣b‾×c‾∣=|\overline{b}\times\overline{c}| =

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  2. Question 2

    13 May 2026 S1

    89
    If the volume of a tetrahedron with coterminous edges a⃗,b⃗\vec{a}, \vec{b} and c⃗\vec{c}, (where a⃗\vec{a} is a unit vector) is 1313 cubic units and the angle between a⃗\vec{a} and b⃗×c⃗\vec{b} \times \vec{c} is π3\dfrac{\pi}{3}, then ∣b⃗×c⃗∣|\vec{b} \times \vec{c}| is

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