Last updated at May 29, 2018 by Teachoo

Transcript

Ex 10.4, 8 If either 𝑎 = 0 or 𝑏 = 0, then 𝑎 × 𝑏 = 0 . Is the converse true? Justify your answer with an example. Converse : If 𝑎 × 𝑏 = 0, then either 𝑎 = 0 or 𝑏 = 0 𝑎 × 𝑏 = 𝑎 𝑏 sin θ 𝑛 where, θ = angle between 𝑎 and 𝑏 𝑛 = unit vector perpendicular to 𝑎 𝜀 𝑏 Let 𝑎 = 1 𝑖 + 1 𝑗 + 1 𝑘 & 𝑏 = 2 𝑖 + 2 𝑗 + 2 𝑘 𝑎 × 𝑏 = 𝑖 𝑗 𝑘111222 = 𝑖 (1 × 2 − 2 × 1) − 𝑗 (1 × 2 −2 × 1) + 𝑘 (1 × 2 − 2 × 1) + 𝑘(1 × 2 − 2 × 1) = 𝑖 (2 − 2) − 𝑗 (2 −2) + 𝑘 (2 − 2) = 0 𝑖 − 0 𝑗 + 0 𝑘 = 0 Here, 𝑎 ≠ 0 & 𝑏≠ 0 But 𝑎 × 𝑏 = 0 Therefore, converse is not true.

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.