# 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

Supplementary examples and questions from CBSE

Supplementary Example 1
Deleted for CBSE Board 2021 Exams only

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 You are here

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

Supplementary Exercise Q10 Deleted for CBSE Board 2021 Exams only

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.