Question

If two lines L1 and L2 are having direction cosines \(l_1,m_1,n_1 \,and \,l_2,m_2,n_2\) respectively, then what is the angle between the two lines?

(a) cot⁡θ=\(\left |l_1 \,l_2+m_1 \,m_2+n_1 \,n_2\right |\)

(b) sin⁡θ=\(\left |l_1 \,l_2+m_1 \,n_2+n_1 \,m_2\right |\)

(c) tan⁡θ=\(\left |l_1 \,l_2+m_1 \,m_2+n_1 \,n_2\right |\)

(d) cos⁡θ=\(\left |l_1 \,l_2+m_1 \,m_2+n_1 \,n_2\right |\)

The question was asked during an interview.

Query is from Three Dimensional Geometry topic in portion Three Dimensional Geometry of Mathematics – Class 12

Answer 1

Correct answer is (d) cos⁡θ=\(\left |l_1 \,l_2+m_1 \,m_2+n_1 \,n_2\right |\)

For explanation: If two lines L1 and L2 are having direction cosines \(l_1,m_1,n_1 \,and \,l_2,m_2,n_2\) respectively, then the angle between the lines is given by

cos⁡θ=\(\left |l_1 \,l_2+m_1 \,m_2+n_1 \,n_2\right |\)