Find k if A⃗=î+ĵ+k̂, B⃗=2î-ĵ+3k̂, and C⃗=3î+kĵ+4k̂ are coplanar.
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Find k if A⃗=î+ĵ+k̂, B⃗=2î-ĵ+3k̂, and C⃗=3î+kĵ+4k̂ are coplanar.

G1 Physics · Accepted Answer

Coplanarity requires determinant |1 1 1; 2 −1 3; 3k̂ 4|=0. Expansion gives (−4−3k̂)−(8−9)+(2k+3)=−k. Hence k=0.