Posts for Tag: Vector

Vector Formulas – HSC Math

$\A↖{→}.\B↖{→} = \AB \cosθ$ $∴ \A \cosθ={|\A↖{→}.\B↖{→}|}/\B, \Projection \of \A↖{→} \on \B↖{→}$ $∴ \B \cosθ={|\A↖{→}.\B↖{→}|}/\A, \Projection \of \B↖{→} \on \A↖{→}$ $\A↖{→}.\B↖{→} = \A_x\B_x+\A_y\B_y+A_z\B_z$ $|\A↖{→}\x\B↖{→}| = \AB \sinθ$ $[\A↖{→}\x\B↖{→}] = |\table \i↖{→}, \j↖{→}, \k↖{→};\A_x,\A_y,\A_z;\B_x,\B_y,\B_z|$ $\i↖{→}.\i↖{→} = \j↖{→}.\j↖{→}=\k↖{→}.\k↖{→}=1$ [$∵\cos0^o=1$] $\i↖{→}.\j↖{→} = \j↖{→}.\k↖{→}=\k↖{→}.\i↖{→}=0$ [$∵\cos90^o=0$] $\i↖{→}\x\i↖{→} = \j↖{→}\x\j↖{→}=\k↖{→}\x\k↖{→}=0↖{→}$ [$∵\sin0^o=0$] $\i↖{→}\x\j↖{→} = \k↖{→}$ $\j↖{→}\x\k↖{→} = \i↖{→}$ $\k↖{→}\x\i↖{→} = \j↖{→}$ $\a↖{→}Read More