Supplementary Exercise Q9
Last updated at May 29, 2018 by Teachoo
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 2 Deleted for CBSE Board 2021 Exams only
Supplementary Example 3 Deleted for CBSE Board 2021 Exams only
Supplementary Example 4 Deleted for CBSE Board 2021 Exams only
Supplementary Example 5 Deleted for CBSE Board 2021 Exams only
Supplementary Example 6 Deleted for CBSE Board 2021 Exams only
Supplementary Exercise Q1 Deleted for CBSE Board 2021 Exams only
Supplementary Exercise Q2 Deleted for CBSE Board 2021 Exams only
Supplementary Exercise Q3 Deleted for CBSE Board 2021 Exams only
Supplementary Exercise Q4 Deleted for CBSE Board 2021 Exams only
Supplementary Exercise Q5 Deleted for CBSE Board 2021 Exams only
Supplementary Exercise Q6 Deleted for CBSE Board 2021 Exams only
Supplementary Exercise Q7 Deleted for CBSE Board 2021 Exams only
Supplementary Exercise Q8 Deleted for CBSE Board 2021 Exams only
Supplementary Exercise Q9 Deleted for CBSE Board 2021 Exams only You are here
Supplementary Exercise Q10 Deleted for CBSE Board 2021 Exams only
Supplementary examples and questions from CBSE
About the Author