If `l_1,m_1,n_1 and l_2,m_2,n_2` are the direction cosines of two rays OA and OB making an angle `theta` then show that the direction cosines of the bisector of `/_AOB` are `(l_1+l_2)/(2cos(theta/2)),(m_1+m_2)/(2cos(theta/2)),(n_1+n_2)/(2cos(theta/2))`

If l_1, m_1, n_2 ; l_2, m_2, n_2, be the direction cosines of two concurrent lines, then direction cosines of the line bisecting the angles between them are proportional to

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_2m_1 .

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_(1)n_(2)-m_(2)n_(1),n_(1)l_(2)-n_(2)l_(1),l_(1)m_(2)-l_(2)m_(1) .

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_(1)n_(2)-m_(2)n_(1),n_(1)l_(2)-n_(2)l_(1),l_(1)m_(2)-l_(2)m_(1) .

If lt l_(1), m_(1), n_(1)gt and lt l_(2), m_(2), n_(2) gt be the direction cosines of two lines L_(1) and L_(2) respectively. If the angle between them is theta , the costheta=?

If ,"l"_1,"m"_1,("\ n")_1("\ and\ l")_2,"m"_2,"n"_2 be the direction cosines of two lines, show that the directioin cosines of the line perpendicular to both them are proportional to ("m"_1("\ n")_2-"m"_2"n"_1),"\ "("n"_1"l"_2-"n"_2"l"_1),"\ "("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.

theta_1 and theta_2 are the inclination of lines L_1a n dL_2 with the x-axis. If L_1a n dL_2 pass through P(x_1,y_1) , then the equation of one of the angle bisector of these lines is (a) (x-x_1)/(cos((theta_1-theta_2)/2))=(y-y_1)/(sin((theta_1-theta_2)/2)) (b) (x-x_1)/(-sin((theta_1-theta_2)/2))=(y-y_1)/(cos((theta_1-theta_2)/2)) (c) (x-x_1)/(sin((theta_1-theta_2)/2))=(y-y_1)/(cos((theta_1-theta_2)/2)) (d) (x-x_1)/(-sin((theta_1-theta_2)/2))=(y-y_1)/(cos((theta_1-theta_2)/2))

sum_(n=1)^ootan(theta/(2^n))/(2^(n-1)cos(theta/(2^(n-1)))) is

Find the angle between the line whose direction cosines are given by l+m+n=0a n dl^2+m^2-n^2-0.