AP EAMCET · Maths · Three Dimensional Geometry
Suppose \(\left(l_1, m_1, n_1\right)\) and \(\left(l_2, m_2, n_2\right)\) are the directional cosines of two lines and \(\theta\) is the angle between them and \(\cos \theta= \pm\left(l_1 l_2+m_1 m_2+n_1 n_2\right)\). Let \(A=(1,-2,3)\), \(B=(3,1,-3)\) and \(C=(-3,1,3)\) be the vertices of \(\triangle A B C\). Then, \(\cos A=\)
- A \(-\frac{1}{35}\)
- B \(\frac{1}{7}\)
- C \(-\frac{1}{7}\)
- D \(\frac{1}{35}\)
Answer & Solution
Correct Answer
(D) \(\frac{1}{35}\)
Step-by-step Solution
Detailed explanation
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…
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