Question

If \[(l_1,m_1,n_1)\] and \[(l_2,m_2,n_2)\] are direction cosines of two lines, then \[\cos\theta\] equals:

विकल्प

• \[|l_1l_2+m_1m_2+n_1n_2|\]

• \[\left|\frac{l_1l_2+m_1m_2+n_1n_2}{\sqrt{l_1^2+m_1^2+n_1^2}\sqrt{l_2^2+m_2^2+n_2^2}}\right|\]

• \[\sqrt{(l_1m_2-l_2m_1)^2+(m_1n_2-m_2n_1)^2+(n_1l_2-n_2l_1)^2}\]

• \[l_1+l_2+m_1+m_2+n_1+n_2\]

Answer 1

Direction cosines are components of unit direction vectors. Therefore, their dot product directly gives \[\cos\theta\], with an absolute value for the acute angle.