JEE Main 202311 Apr, Evening shiftMathematicsMediumVector Algebra184× since 2002If four distinct points with position vectors a⃗,b⃗,c⃗\vec{a}, \vec{b}, \vec{c}a,b,c and d⃗\vec{d}d are coplanar, then [a⃗ b⃗ c⃗][\vec{a} \,\,\vec{b} \,\,\vec{c}][abc] is equal to :AOption A. [d⃗ b⃗ a⃗]+[a⃗ c⃗ d⃗]+[d⃗ b⃗ c⃗][\vec{d} \,\,\,\,\,\vec{b} \,\,\,\,\,\vec{a}]+[\vec{a} \,\,\,\,\,\vec{c} \,\,\,\,\,\vec{d}]+[\vec{d} \,\,\,\,\,\vec{b} \,\,\,\,\,\vec{c}][dba]+[acd]+[dbc]BOption B. [b⃗ c⃗ d⃗]+[d⃗ a⃗ c⃗]+[d⃗ b⃗ a⃗][\vec{b} \,\,\,\,\,\vec{c} \,\,\,\,\,\vec{d}]+[\vec{d} \,\,\,\,\,\vec{a} \,\,\,\,\,\vec{c}]+[\vec{d} \,\,\,\,\,\vec{b} \,\,\,\,\,\vec{a}][bcd]+[dac]+[dba]COption C. [a⃗ d⃗ b⃗]+[d⃗ c⃗ a⃗]+[d⃗ b⃗ c⃗][\vec{a} \,\,\,\,\,\vec{d} \,\,\,\,\,\vec{b}]+[\vec{d} \,\,\,\,\,\vec{c} \,\,\,\,\,\vec{a}]+[\vec{d} \,\,\,\,\,\vec{b} \,\,\,\,\,\vec{c}][adb]+[dca]+[dbc]DOption D. [d⃗ c⃗ a⃗]+[b⃗ d⃗ a⃗]+[c⃗ d⃗ b⃗][\vec{d} \,\,\,\,\,\vec{c} \,\,\,\,\,\vec{a}]+[\vec{b} \,\,\,\,\,\vec{d} \,\,\,\,\,\vec{a}]+[\vec{c} \,\,\,\,\,\vec{d} \,\,\,\,\,\vec{b}][dca]+[bda]+[cdb]CheckSkip · show solution
