Suppose $\left(l_1, m_1, n_1 ight)$ and $\left(l_2, m_2, n_2 ight)$ are the directional cosines of two lines and $ heta$ is the angle between them and $\cos heta= \pm\left(l_1 l_2+m_1 m_2+n_1 n_2 ight)$. Let $A=(1,-2,3)$, $B=(3,1,-3)$ and $C=(-3,1,3)$ be the vertices of $ riangle A B C$.…

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Suppose $\left(l_1, m_1, n_1ight)$ and $\left(l_2, m_2, n_2ight)$ are the directional cosines of two lines and $	heta$ is the angle between them and $\cos 	heta= \pm\left(l_1 l_2+m_1 m_2+n_1 n_2ight)$. Let $A=(1,-2,3)$, $B=(3,1,-3)$ and $C=(-3,1,3)$ be the vertices of $	riangle A B C$. Then, $\cos A=$

Aicharya · Accepted Answer

Let DC's of $A B$ and $A C$ are $l_1, m_1, n_1$ and $l_2, m_2, n_2$ respectively. DR's of $A B: 2,3,-6$ $\mathrm{DR}^{\prime} \mathrm{s}$ of $A C:-4,3,0$ $\therefore \quad l_1=\frac{2}{7}, m_1=\frac{3}{7}, n_1=\frac{-6}{7}$ and $l_2=-\frac{4}{5}, m_2=\frac{3}{5}, n_2=0$ $\therefore \quad \cos A=\left(l_1 l_2+m_1 m_2+n_1 n_2\right)$ $=\frac{2}{7} \times\left(\frac{-4}{5}\right)+\frac{3}{7} \times \frac{3}{5}+0=\frac{1}{35}$

Suppose $\left(l_1, m_1, n_1\right)$ and $\left(l_2, m_2, n_2\right)$ are the directional cosines of two…

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