giúp em vs ạ cho $(\alpha):A_1x+By+C_1z+D_1=0$ và $M_0(x_0;y_0;z_0)$,$(B):A_2+B_2y+C_2z+D_2=0$,$cos(\alpha,\beta))=?$,$d(\alpha,\varphi))=?$,Từ $d(M_0,(\alpha))=?$,$(\alpha)//\beta)\Leftrightarrow$,(2) cắt (B) $\leftrightarrow$,$(\alpha\equiv(\beta)\Leftrightarrow$,. M cầu (S) $\frac{có~tàm~I(a^\prime,b^\prime,c)}{có~bK~r}$ có dạng :?,có bK,$\bullet MC(S):x^2+y^2+z^2-2ax-2by-2cz+d=0$,có tâm $I()?,bkr=?$ $)?,bkr=?.$,TÂN VĨNH TIẾN

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Accepted Answer

$\displaystyle \begin{array}{{>{\displaystyle}l}}
( \alpha ) =A_{1} x+B_{1} y+C_{1} z+D_{1} =0\
( \beta ) =A_{2} x+B_{2} y+C_{2} z+D\ _{2} =0\
a,cos(( \alpha ) ;( \beta )) =\frac{|A_{1} .A_{2} +B_{1} .B_{2} +C_{1} .C_{2} |}{\sqrt{A_{1}^{2} +B_{1}^{2} +C_{1}^{2}} .\sqrt{A_{2}^{2} +B_{2}^{2} +C_{2}^{2}}}\
b,ta\ có\ :\ E\left( 0,0,\frac{-D_{1}}{C_{1}} ight) \ thuộc\ mp( \alpha )\
d(( \alpha ) ,( \beta )) =\frac{|A_{2} .0+B_{2} .0+C_{2} .\left(\frac{-D_{1}}{C_{1}} ight) |}{\sqrt{A_{2}^{2} +B_{2}^{2} +C_{2}^{2}}}\
c,d( M_{0} ,\ ( \alpha )) =\frac{|A_{1} .x_{0} +B_{1} .y_{0} +C_{1} .z_{0} +D_{1} |}{\sqrt{A_{1}^{2} +B_{1}^{2} +C_{1}^{2}}}\
d,( \alpha ) \ song\ song\ ( \beta )\
\frac{A_{1}}{A_{2}} =\frac{B_{1}}{B_{2}} =\frac{C_{1}}{C2}\
e,\ ( \alpha ) \ cắt\ ( \beta ) \ :\ ( A_{1} ,B_{1} ,C_{1}) eq \ k.\ ( A_{2} ,B_{2} ,C_{2})\
f,\ \ ( \alpha ) \ \equiv \ ( \beta ) \ :\ ( A_{1} ,B_{1} ,C_{1}) =\ k.\ ( A_{2} ,B_{2} ,C_{2}) \ và\ D_{1} =k.D_{2}\
\end{array}$