# 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 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 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.