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Supplementary Exercise Q9
Last updated at May 29, 2018 by Teachoo
Transcript
Supplementary Exercise Q9 Show that if the vectors 𝑎, 𝑏 and 𝑐 are co-planar, then 𝑎 + 𝑏, 𝑏 + 𝑐 and 𝑐 + 𝑎 are also co-planar Vectors 𝑎, 𝑏, 𝑐 are coplanar if 𝑎 𝑏 𝑐 = 0 Finding 𝑎 + 𝑏 𝑏+ 𝑐 𝑐+ 𝑎 𝑎 + 𝑏 𝑏+ 𝑐 𝑐+ 𝑎 = ( 𝑎 + 𝑏). ( 𝑏+ 𝑐) × ( 𝑐+ 𝑎) = ( 𝑎 + 𝑏). ( 𝑏× 𝑐) + ( 𝑏× 𝑎)+( 𝒄× 𝒄) + ( 𝑐× 𝑎) = ( 𝑎+ 𝑏). 𝑏× 𝑐) + ( 𝑏× 𝑎 + 0 + ( 𝑐 × 𝑎) = 𝑎. ( 𝑏 × 𝑐) + 𝑏.( 𝑏 × 𝑐) + 𝑎. ( 𝑏 × 𝑎) + 𝑏.( 𝑏 × 𝑎) + 𝑎.( 𝑐 × 𝑎) + 𝑏.( 𝑐 × 𝑎) = 𝑎, 𝑏, 𝑐 + 𝒃, 𝒃, 𝒄 + 𝒂, 𝒃, 𝒂 + 𝒃, 𝒃, 𝒂 + 𝒂, 𝒄, 𝒂 + 𝑏, 𝑐, 𝑎 = 𝑎, 𝑏, 𝑐 + 0 + 0 + 0 + 0 + 𝑏, 𝑐, 𝑎 = 𝑎, 𝑏, 𝑐 + 𝒃, 𝒄, 𝒂 = 𝑎, 𝑏, 𝑐 + 𝒂, 𝒃, 𝒄 = 2 𝑎, 𝑏, 𝑐 = 2 × 0 = 0 Since 𝑎 + 𝑏 𝑏+ 𝑐 𝑐+ 𝑎 = 0 𝑎 + 𝑏, 𝑏 + 𝑐 and 𝑐 + 𝑎 are also co-planar Hence proved
Supplementary examples and questions from CBSE
Supplementary Example 1
Supplementary Example 2
Supplementary Example 3
Supplementary Example 4
Supplementary Example 5
Supplementary Example 6
Supplementary Exercise Q1
Supplementary Exercise Q2
Supplementary Exercise Q3
Supplementary Exercise Q4
Supplementary Exercise Q5
Supplementary Exercise Q6
Supplementary Exercise Q7
Supplementary Exercise Q8
Supplementary Exercise Q9 You are here
Supplementary Exercise Q10
About the Author
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.