Vector



  • 0_1542141623171_2481916A-162C-4AC2-ADFE-04E78B5674F4.jpeg



  • @Amardeep
    You can write [n^p^m^][\hat{n} \hat{p} \hat{m}][n^p^m^] as [p^m^n^][\hat{p} \hat{m} \hat{n}][p^m^n^]

    Dot and cross in a scalar triple product can be interchanged.

    [p^m^n^]=p^⋅(m^×n^)=∣p^∣∣m^×n^∣cosα[\hat{p} \hat{m} \hat{n}] = \hat{p} \cdot (\hat{m} \times \hat{n}) = |\hat{p}||\hat{m} \times \hat{n}|cos\alpha[p^m^n^]=p^(m^×n^)=p^m^×n^cosα
    =∣p^∣∣(m^∣∣n^∣sinα)cosα=sinαcosα(∵,∣p^∣=∣m^∣=∣n^∣=1)= |\hat{p}||(\hat{m}||\hat{n}|sin\alpha) cos\alpha = sin\alpha cos\alpha (\because, |\hat{p}|=|\hat{m}|=|\hat{n}|=1)=p^(m^n^sinα)cosα=sinαcosα(,p^=m^=n^=1)

    So,
    [n^p^m^]=sinαcosα[\hat{n} \hat{p} \hat{m}] = sin\alpha cos\alpha[n^p^m^]=sinαcosα


Log in to reply
 

Powered by dubbtr | @2020