The cosine of the angle $A$ of the triangle with vertices $A(1,-1,2), B(6,11,2), C(1,2,6)$ is

Question

Aicharya · Accepted Answer

Direction ratios of $\begin{aligned} A B & =6-1,11+1,2-2 \ & =5,12,0\end{aligned}$ Direction ratios of $\begin{aligned} A C & =1-1,2+1,6-2 \ & =0,3,4\end{aligned}$ Now, $\begin{aligned} \cos A & =\frac{a_1 a_2+b_1 b_2+c_1 c_2}{\sqrt{a_1^2+b_1^2+c_1^2} \sqrt{a_2^2+b_2^2+c_2^2}} \ \Rightarrow \quad \cos A & =\frac{5 	imes 0+12 	imes 3+0 	imes 4}{\sqrt{25+144+0} \sqrt{0+9+16}} \ & =\frac{36}{13 	imes 5} \ & =\frac{36}{65}\end{aligned}$

The cosine of the angle $A$ of the triangle with vertices $A(1,-1,2), B(6,11,2), C(1,2,6)$ is

Solution