Given A⃗=î+2ĵ-k̂, B⃗=2î-ĵ+3k̂, C⃗=pî+3ĵ+2k̂, find p for coplanarity.
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Given A⃗=î+2ĵ-k̂, B⃗=2î-ĵ+3k̂, C⃗=pî+3ĵ+2k̂, find p for coplanarity.

G1 Physics · Accepted Answer

B×C=(−11,3p−4,p+6). A·(B×C)=−11+2(3p−4)−(p+6)=5p−25. Coplanarity requires zero, so p=5. The parallelepiped volume is then zero.