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IF `veca=2veci+3vecj+4veck and vecb =4veci+3vecj+2veck` find the angle between `veca and vecb`. |
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Answer» We have `veca.vecb=ab costheta` or `costheta= (veca.vecb)/(ab)` where `theta` is the angle between `veca and vecb` Now `veca.veb=a_xb_x+a_yb_y+a_zb^z` `=2xx4+3xx3+4xx2=25` Also, `veca=sqrt(a_x^2+a_y^2+a_z^2) `=sqrt(4+9+16)= sqrt29` and ` b= sqrt(b_x^2+b_u^2+b_z^2= sqrt(16+9+4)= sqrt(16+9+4)=sqrt29` Thrus, `costheta = 25/29` `or, `theta= cos^-1 (25/29)`. |
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