Supplementary Example 4
Last updated at May 29, 2018 by Teachoo
Last updated at May 29, 2018 by Teachoo
Transcript
Supplementary Example 4 Show that the vectors 𝑎 = 𝑖 − 2 𝑗 + 3 𝑘, 𝑏 = −2 𝑖 + 3 𝑗 − 4 𝑘 and 𝑐 = 𝑖 − 3 𝑗 + 𝜆 𝑘 are co-planar if 𝜆 = 5 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 + λ 𝑘 𝑎 𝑏 𝑐 = 1−23−23−41−3𝜆 0 = 1 3×λ−(−3×−4) − (−2) −2×λ−(1×−4) + 3 2×−3−(1×3) 0 = 1 3λ−12+2 −2λ−(−4)+3 6−3 0 = 3λ – 12 – 4λ + 8 + 9 0 = – λ + 5 𝝀 = 5 Therefore, 𝑎,𝑏, 𝑐 are coplanar if λ = 5
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Supplementary examples and questions from CBSE
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