cosα=a12​+b12​​⋅a22​+b22​​∣a1​a2​+b1​b2​∣​

Với:

• Δ:3x+4y+7=0⇒a1=3,b1=4\Delta : 3x + 4y + 7 = 0 \Rightarrow a_1 = 3, b_1 = 4Δ:3x+4y+7=0⇒a1​=3,b1​=4.

• Δ1:5x−12y+7=0⇒a2=5,b2=−12\Delta_1 : 5x - 12y + 7 = 0 \Rightarrow a_2 = 5, b_2 = -12Δ1​:5x−12y+7=0⇒a2​=5,b2​=−12.

Tính $\cos \alpha$:

cos⁡α=∣(3)(5)+(4)(−12)∣32+42⋅52+(−12)2\cos \alpha = \frac{|(3)(5) + (4)(-12)|}{\sqrt{3^2 + 4^2} \cdot \sqrt{5^2 + (-12)^2}}cosα=32+42​⋅52+(−12)2​∣(3)(5)+(4)(−12)∣​ =∣15−48∣9+16⋅25+144= \frac{|15 - 48|}{\sqrt{9 + 16} \cdot \sqrt{25 + 144}}=9+16​⋅25+144​∣15−48∣​ =∣−33∣25⋅169= \frac{| -33 |}{\sqrt{25} \cdot \sqrt{169}}=25​⋅169​∣−33∣​ =335×13=3365= \frac{33}{5 \times 13} = \frac{33}{65}=5×1333​=6533​