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Last updated at May 29, 2018 by Teachoo

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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
Not in Syllabus - CBSE Exams 2021

Supplementary Example 2 Not in Syllabus - CBSE Exams 2021

Supplementary Example 3 Not in Syllabus - CBSE Exams 2021

Supplementary Example 4 Not in Syllabus - CBSE Exams 2021

Supplementary Example 5 Not in Syllabus - CBSE Exams 2021

Supplementary Example 6 Not in Syllabus - CBSE Exams 2021

Supplementary Exercise Q1 Not in Syllabus - CBSE Exams 2021

Supplementary Exercise Q2 Not in Syllabus - CBSE Exams 2021

Supplementary Exercise Q3 Not in Syllabus - CBSE Exams 2021

Supplementary Exercise Q4 Not in Syllabus - CBSE Exams 2021

Supplementary Exercise Q5 Not in Syllabus - CBSE Exams 2021

Supplementary Exercise Q6 Not in Syllabus - CBSE Exams 2021

Supplementary Exercise Q7 Not in Syllabus - CBSE Exams 2021

Supplementary Exercise Q8 Not in Syllabus - CBSE Exams 2021

Supplementary Exercise Q9 Not in Syllabus - CBSE Exams 2021 You are here

Supplementary Exercise Q10 Not in Syllabus - CBSE Exams 2021

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.