Vector Formulas – HSC Math

Posted In: Mathematics
  1. $\A↖{→}.\B↖{→} = \AB \cosθ$
    $∴ \A \cosθ={|\A↖{→}.\B↖{→}|}/\B, \Projection \of \A↖{→} \on \B↖{→}$
    $∴ \B \cosθ={|\A↖{→}.\B↖{→}|}/\A, \Projection \of \B↖{→} \on \A↖{→}$
  2. $\A↖{→}.\B↖{→} = \A_x\B_x+\A_y\B_y+A_z\B_z$
  3. $|\A↖{→}\x\B↖{→}| = \AB \sinθ$
  4. $[\A↖{→}\x\B↖{→}] = |\table \i↖{→}, \j↖{→}, \k↖{→};\A_x,\A_y,\A_z;\B_x,\B_y,\B_z|$
  5. $\i↖{→}.\i↖{→} = \j↖{→}.\j↖{→}=\k↖{→}.\k↖{→}=1$ [$∵\cos0^o=1$]
  6. $\i↖{→}.\j↖{→} = \j↖{→}.\k↖{→}=\k↖{→}.\i↖{→}=0$ [$∵\cos90^o=0$]
  7. $\i↖{→}\x\i↖{→} = \j↖{→}\x\j↖{→}=\k↖{→}\x\k↖{→}=0↖{→}$ [$∵\sin0^o=0$]
    $\i↖{→}\x\j↖{→} = \k↖{→}$
    $\j↖{→}\x\k↖{→} = \i↖{→}$
    $\k↖{→}\x\i↖{→} = \j↖{→}$
  8. $\a↖{→} = \A↖{→}/{|\A↖{→}|} = {\A_x\i↖{→}+\A_y\j↖{→}+\A_z\k↖{→}}/√{\A_x^2+\A_y^2+\A_z^2}$
  9. $\A↖{→}+\B↖{→} = (\A_x+\B_x)\i↖{→}+(\A_y+\B_y)\j↖{→}+(\A_z+\B_z)\k↖{→}$
  10. $\n↖{→}=\R↖{→}/{|\R↖{→}|}$
  11. $\η↖{→}=±{\A↖{→}+\B↖{→}}/{|\A↖{→}+\B↖{→}|}$
  12. $\If \A↖{→} \and \B↖{→} \are \parallel, \A_x/\B_x=\A_y/\B_y=\A_z/\B_z$

Post Tags: HSC | Vector


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