Question

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

• A. $\frac{63}{65}$
• B. $\frac{36}{65}$
• C. $\frac{16}{65}$
• D. $\frac{13}{64}$

Answer 1

The correct option is B $\frac{36}{65}$

$\overrightarrow{AB}=5\hat{i}+12\hat{j}$

$\overrightarrow{AC}=3\hat{j}+4\hat{k}$

$\overrightarrow{AB}.\overrightarrow{AC}=|AB||AC|cosA$

$36=\sqrt{5^2+{12}^2}\sqrt{3^2+4^2}cosA$

$\frac{36}{13\times 5}=cosA\Rightarrow cosA=\frac{36}{65}$