Supplementary Exercise Q4
Last updated at May 29, 2018 by Teachoo
Last updated at May 29, 2018 by Teachoo
Transcript
Supplementary Exercise Q4 Show that (i) the vectors 𝑎 = 2 𝑖 − 𝑗 + 𝑘, 𝑏 = 𝑖 + 2 𝑗 − 3 𝑘, and 𝑐 = 3 𝑖 − 4 𝑗 + 5 𝑘 are coplanar. Three vectors 𝑎, 𝑏, 𝑐 are coplanar if [ 𝒂, 𝒃, 𝒄 ] = 0 Given, 𝑎 = 2 𝑖 − 𝑗 + 𝑘 𝑏 = 𝑖 + 2 𝑗 − 3 𝑘 𝑐 = 3 𝑖 − 4 𝑗 + 5 𝑘 𝑎,𝑏, 𝑐 = 2−1112−33−45 = 2 2×5−(−4×−3) − (−1) 1×5−(3×−3) + 1 1×−4−(3×2) = 2 10−12+ 5+9 + −4−6 = –4 + 14 – 10 = 0 ∴ 𝒂,𝒃, 𝒄 = 0 Therefore, 𝑎,𝑏 and 𝑐 are coplanar. Supplementary Exercise Q4 Show that (ii) the vectors 𝑎 = 𝑖 − 2 𝑗 + 3 𝑘, 𝑏 = −2 𝑖 + 3 𝑗 − 4 𝑘, and 𝑐 = 𝑖 − 3 𝑗 + 5 𝑘 are coplanar Three vectors 𝑎, 𝑏, 𝑐 are coplanar if [ 𝒂, 𝒃, 𝒄 ] = 0 Given, 𝑎 = 𝑖 − 2 𝑗 + 3 𝑘 𝑏 = −2 𝑖 + 3 𝑗 − 4 𝑘 𝑐 = 𝑖 − 3 𝑗 + 5 𝑘 𝑎,𝑏, 𝑐 = 1−23−23−41−35 = 1 3×5−(−3×4) − (−2) −2×5−(1×−4) + 3 −2×−3−(1×3) = 1 15−12+ 2 −10−(−4 + 3 6−3 = 1(3) + 2 (−6) + 3 (3) = 3 − 12 + 9 = 12 − 12 = 0 ∴ 𝒂,𝒃, 𝒄 = 0 Therefore, 𝑎,𝑏 and 𝑐 are coplanar.
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