If and are the direction cosines of two mutually perpendicular lines

MATHEMATICS · Subjective · CBSE · Mathematics · Vector Algebra · Vector Algebra

Problem

l_1, m_1, n_1

and

l_2, m_2, n_2

are the direction cosines of two mutually perpendicular lines, show that the direction cosines of the line perpendicular to both of them are

m_1 n_2 - m_2 n_1

;

n_1 l_2 - n_2 l_1

;

l_1 m_2 - l_2 m_1