JEE Main 2023 (11 Apr, Shift 2) Maths Q17: Triple Products

Question

If four distinct points with position vectors $\vec{a}, \vec{b}, \vec{c}$ and $\vec{d}$ are coplanar, then $[\vec{a}\ \vec{b}\ \vec{c}]$ is equal to

Accepted Answer

Option 2: $[\vec{d}\ \vec{c}\ \vec{a}] + [\vec{b}\ \vec{d}\ \vec{a}] + [\vec{c}\ \vec{d}\ \vec{b}]$

Answer

$[\vec{d}\ \vec{b}\ \vec{a}] + [\vec{a}\ \vec{c}\ \vec{d}] + [\vec{d}\ \vec{b}\ \vec{c}]$

Answer

$[\vec{d}\ \vec{c}\ \vec{a}] + [\vec{b}\ \vec{d}\ \vec{a}] + [\vec{c}\ \vec{d}\ \vec{b}]$

Answer

$[\vec{a}\ \vec{d}\ \vec{b}] + [\vec{d}\ \vec{c}\ \vec{a}] + [\vec{d}\ \vec{b}\ \vec{c}]$

Answer

$[\vec{b}\ \vec{c}\ \vec{d}] + [\vec{d}\ \vec{a}\ \vec{c}] + [\vec{d}\ \vec{b}\ \vec{a}]$

JEE Main 11 April 2023, Shift 2, Maths Q17