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MCQMediumJEE Main 2023 · 11 April, Shift 2Cross Product

Mathematics Question from JEE Main 2023 · 11 April, Shift 2

If four distinct points with position vectors a⃗,b⃗,c⃗, and d⃗\vec{a}, \vec{b}, \vec{c}, \text{ and } \vec{d} are coplanar, then [a⃗b⃗c⃗][\vec{a}\vec{b}\vec{c}] is equal to:

  • A

    [d⃗c⃗a⃗]+[b⃗d⃗a⃗]+[c⃗d⃗b⃗][\vec{d}\vec{c}\vec{a}] + [\vec{b}\vec{d}\vec{a}] + [\vec{c}\vec{d}\vec{b}]

  • B

    [d⃗b⃗a⃗]+[a⃗c⃗d⃗]+[d⃗b⃗c⃗][\vec{d}\vec{b}\vec{a}] + [\vec{a}\vec{c}\vec{d}] + [\vec{d}\vec{b}\vec{c}]

  • C

    [a⃗d⃗b⃗]+[d⃗c⃗a⃗]+[d⃗b⃗c⃗][\vec{a}\vec{d}\vec{b}] + [\vec{d}\vec{c}\vec{a}] + [\vec{d}\vec{b}\vec{c}]

  • D

    [b⃗c⃗d⃗]+[d⃗a⃗c⃗]+[d⃗b⃗a⃗][\vec{b}\vec{c}\vec{d}] + [\vec{d}\vec{a}\vec{c}] + [\vec{d}\vec{b}\vec{a}]

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