Misc 4 - If a = b + c, then is it true that |a| = |b| + |c| - Addition(resultant) of vectors

Slide12.JPG

  1. Chapter 10 Class 12 Vector Algebra
  2. Serial order wise
Ask Download

Transcript

Misc 4 If 𝑎﷯ = 𝑏﷯ + 𝑐﷯ , then is it true that | 𝑎﷯|=| 𝑏﷯| + | 𝑐﷯| Justify your answer. Given, 𝑎﷯ = 𝑏﷯ + 𝑐﷯ Let 𝑏﷯ = 1 𝑖﷯ + 2 𝑗﷯ + 3 𝑘﷯ & 𝑐﷯ = 2 𝑖﷯ − 1 𝑗﷯ − 2 𝑘﷯ 𝑎﷯ = ( 𝑏﷯ + 𝑐﷯) = (1 + 2) 𝑖﷯ + (2 − 1) 𝑗﷯ + (3 − 2) 𝑘﷯ = 3 𝑖﷯ + 1 𝑗﷯ + 1 𝑘﷯ So, 𝑎﷯ = 3 𝑖﷯ + 1 𝑗﷯ + 1 𝑘﷯ Magnitude of 𝑎﷯ = ﷮32+ 1﷮2﷯+ 1﷮2﷯﷯ 𝑎﷯﷯ = ﷮9+1+1﷯ = ﷮11﷯ Magnitude of 𝑏﷯ = ﷮12+22+32﷯ 𝑏﷯﷯ = ﷮1+4+9﷯ = ﷮14﷯ Magnitude of 𝑐﷯ = ﷮22+(−1)2+(−2)2﷯ 𝑐﷯﷯ = ﷮4+1+4﷯ = ﷮9﷯ = 3 Now, 𝑏﷯﷯ + 𝑐﷯﷯ = ﷮14﷯ + 3 ≠ ﷮11﷯ ≠ 𝑎﷯﷯ So, 𝑎﷯﷯≠ 𝑏﷯﷯ + 𝑐﷯﷯ Hence, false.

About the Author

Davneet Singh's photo - Teacher, Computer Engineer, Marketer
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.