If (a_1, b_1, c_1) and (a_2, b_2, c_2) are th | vedclass

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(B) The direction cosines of two lines are given as $(a_1, b_1, c_1)$ and $(a_2, b_2, c_2)$.Since these are direction cosines,we have the property $a_

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$|a_1 a_2 + b_1 b_2 + c_1 c_2|$

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(B) The direction cosines of two lines are given as $(a_1, b_1, c_1)$ and $(a_2, b_2, c_2)$.Since these are direction cosines,we have the property $a_1^2 + b_1^2 + c_1^2 = 1$ and $a_2^2 + b_2^2 + c_2^2 = 1$.The angle $	heta$ between two lines with direction cosines $(l_1, m_1, n_1)$ and $(l_2, m_2, n_2)$ is given by $\cos 	heta = |l_1 l_2 + m_1 m_2 + n_1 n_2|$.Substituting the given values,we get $\cos 	heta = |a_1 a_2 + b_1 b_2 + c_1 c_2|$.Since the denominator is $\sqrt{a_1^2 + b_1^2 + c_1^2} \cdot \sqrt{a_2^2 + b_2^2 + c_2^2} = \sqrt{1} \cdot \sqrt{1} = 1$,the expression simplifies to $|a_1 a_2 + b_1 b_2 + c_1 c_2|$.

If $(a_1, b_1, c_1)$ and $(a_2, b_2, c_2)$ are the direction cosines of two lines making an angle $\theta$ with each other,then $\cos \theta =$

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