If the direction cosines of a straight line are `l, m and n`,then prove that `l^2 + m^2 + n^2 = 1`.

If l,m,n are direction cosines of the line then -l,-m,-n can be

If l_(1), m_(1), n_(1) and l_(2), m_(2), n_(2) are direction cosines of two mutually perpendicular straight lines, then prove that the direction cosines of the straight line which is perpendicular to both the given lines are pm (m_(1)n_(2)-m_(2)n_(1)), pm (n_(1)l_(2)-n_(2)l_(1)), pm (l_(1)m_(2)-l_(2)m_(1))

If the direction cosines of two lines are l_(1), m_(1), n_(1) and l_(2), m_(2), n_(2) , then find the direction cosine of a line perpendicular to these lines.

If the direction cosines of two lines are l_(1), m_(1), n_(1) and l_(2), m_(2), n_(2) , then find the direction cosine of a line perpendicular to these lines.

If the direction cosines of two lines are l_(1), m_(1), n_(1) and l_(2), m_(2), n_(2) , then find the direction cosine of a line perpendicular to these lines. a) l_(1)+l_(2),m_(1)+m_(2),n_(1)+n_(2) b) l_(1)-l_(2),m_(1)-m_(2),n_(1)-n_(2) c) m_(1)n_(2)-m_(2)n_(1),n_(1)l_(2)-n_(2)l_(1),l_(1)m_(2)-l_(2)m_(1) d) l_(1)+2l_(2),m_(1)+2m_(2),n_(1)+2n_(2)

Find the angle between the lines whose direction cosines are given by the equation l + m + n = 0 and l^2 + m^2 - n^2 = 0.

If 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 these are m_1n_2 - m_2n_1, n_1l_2 - n_2l_1, l_1m_2-l_2-m_1