Giải thích các bước giải:
\(\underset{AB}(-2;-8) \rightarrow AB=2\sqrt{17}\)
\(\underset{AC}(-3;3) \rightarrow AC=3\sqrt{2}\)
\(\underset{BC}(-1;11) \rightarrow BC=\sqrt{122}\)
a. CosB=\(\frac {AB^{2}+BC^{2}-AC^{2}}{2AB.BC}=\frac{(2\sqrt{17})^{2}+\sqrt{122}^{2}-(3\sqrt{2})^{2}}{2.2\sqrt{17}.\sqrt{122}}=0,94\)
\(\rightarrow \widehat{B}=19°\)
b.
\(\underset{n}\) : chỉ phương
\(\underset{a}\) :pháp tuyến
PTTQ AB:
\(\underset{n}(-2;-8)\)
\(\rightarrow \underset{a}(-8;2)\)
A(6;-2)
AB: \(-8(x-6)+2(y+2)=0\)
\(\rightarrow -8x+2y+52=0\)
PTTQ AC:
\(\underset{n}(-3;3)\)
\(\rightarrow \underset{a}(3;3)\)
A(6;-2)
AC: \(3(x-6)-3(y+2)=0\)
\(\rightarrow 3x-3y-24=0\)
\(\rightarrow x-y-8=0\)
PTTQ BC:
\(\underset{n}(-1;11)\)
\(\rightarrow \underset{a}(11;1)\)
C(3;1)
BC: \(3(x-11)+1(y-1)=0\)
\(\rightarrow 3x+y-34=0\)
c. PTTQ CM:
M(5;-6) [Ấp dụng ct Tính tạo độ trung điểm]
C(3;1)
\(\underset{a}(7;2)\)
CM: \(7(x-3)+2(y-1)=0\)
\(\rightarrow 7x+2y-23=0\)
