The cosine of the angle A of the triangle wit | vedclass

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(B) The direction ratios of the vector $\vec{AB}$ are $(6-1, 11-(-1), 2-2) = (5, 12, 0)$.The direction ratios of the vector $\vec{AC}$ are $(1-1, 2-(-

Vedclass · Accepted Answer

$36 / 65$

Vedclass · Answer

(B) The direction ratios of the vector $\vec{AB}$ are $(6-1, 11-(-1), 2-2) = (5, 12, 0)$.The direction ratios of the vector $\vec{AC}$ are $(1-1, 2-(-1), 6-2) = (0, 3, 4)$.The cosine of the angle $A$ between vectors $\vec{AB}$ and $\vec{AC}$ is given by the formula:$\cos A = \frac{a_1 a_2 + b_1 b_2 + c_1 c_2}{\sqrt{a_1^2 + b_1^2 + c_1^2} \sqrt{a_2^2 + b_2^2 + c_2^2}}$Substituting the values:$\cos A = \frac{(5)(0) + (12)(3) + (0)(4)}{\sqrt{5^2 + 12^2 + 0^2} \sqrt{0^2 + 3^2 + 4^2}}$$\cos A = \frac{0 + 36 + 0}{\sqrt{25 + 144 + 0} \sqrt{0 + 9 + 16}}$$\cos A = \frac{36}{\sqrt{169} \sqrt{25}}$$\cos A = \frac{36}{13 	imes 5} = \frac{36}{65}$.

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

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