# Supplementary Exercise Q4

Last updated at May 29, 2018 by Teachoo

Last updated at May 29, 2018 by Teachoo

Transcript

Supplementary Exercise Q4 Show that (i) the vectors 𝑎 = 2 𝑖 − 𝑗 + 𝑘, 𝑏 = 𝑖 + 2 𝑗 − 3 𝑘, and 𝑐 = 3 𝑖 − 4 𝑗 + 5 𝑘 are coplanar. Three vectors 𝑎, 𝑏, 𝑐 are coplanar if [ 𝒂, 𝒃, 𝒄 ] = 0 Given, 𝑎 = 2 𝑖 − 𝑗 + 𝑘 𝑏 = 𝑖 + 2 𝑗 − 3 𝑘 𝑐 = 3 𝑖 − 4 𝑗 + 5 𝑘 𝑎,𝑏, 𝑐 = 2−1112−33−45 = 2 2×5−(−4×−3) − (−1) 1×5−(3×−3) + 1 1×−4−(3×2) = 2 10−12+ 5+9 + −4−6 = –4 + 14 – 10 = 0 ∴ 𝒂,𝒃, 𝒄 = 0 Therefore, 𝑎,𝑏 and 𝑐 are coplanar. Supplementary Exercise Q4 Show that (ii) the vectors 𝑎 = 𝑖 − 2 𝑗 + 3 𝑘, 𝑏 = −2 𝑖 + 3 𝑗 − 4 𝑘, and 𝑐 = 𝑖 − 3 𝑗 + 5 𝑘 are coplanar 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 + 5 𝑘 𝑎,𝑏, 𝑐 = 1−23−23−41−35 = 1 3×5−(−3×4) − (−2) −2×5−(1×−4) + 3 −2×−3−(1×3) = 1 15−12+ 2 −10−(−4 + 3 6−3 = 1(3) + 2 (−6) + 3 (3) = 3 − 12 + 9 = 12 − 12 = 0 ∴ 𝒂,𝒃, 𝒄 = 0 Therefore, 𝑎,𝑏 and 𝑐 are coplanar.

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 You are here

Supplementary Exercise Q5

Supplementary Exercise Q6

Supplementary Exercise Q7

Supplementary Exercise Q8

Supplementary Exercise Q9

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.