If two lines are parallel to each other, then which of the following is true? (if \(\left(l_1, m_1,…

If two lines are parallel to each other, then which of the following is true? (if \(\left(l_1, m_1, n_1\right)\) and \(\left(l_2, m_2, n_2\right)\) are direction cosines of the two lines).
  1. \(I_1 I_2+m_1 m_2+n_1 n_2=0\)
  2. \(\Sigma\left(l_1 l_2-m_2 m_1\right)^2=0\)
  3. \(\frac{l_1}{l_2}=\frac{m_1}{m_2}=\frac{n_1}{n_2}\)
  4. \(l_1 l_2+m_1 m_2+n_1 n_2=1\)

Solution

The two lines having direction \(\operatorname{cosines} l_1, m_1, n_1\) and \(l_2, m_2, n_2\) respectively are parallel to each other, then \(\frac{l_1}{l_2}=\frac{m_1}{m_2}=\frac{n_1}{n_2}\) Hence, option (c) is correct.

Asked in: AP EAMCET 2020 (21 Sep Shift 2)

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