If L1,M1,N1 and L2,M2,N2 are the direction cosines of two mutually perpendicular lines then find the direction cosines of a line perpendicular to both.

the direction cosines of the line perpendicular to any two lines can be obtained by the cross product of the direction vectors of the given lines and dividing the result obtained by its magnitude.The three cosines are then the three components of the final unit vector.

direction vector of line1: L1i+M1j+N1k =v1(say)

direction vector of line2: L2i+M2j+L2k =v2(say)

v3=v1crossv2.=ai+bj+ck(say)

direction cosines of the perpendicular line= L3=+/-(a/|v3|)

                                                                                M3=+/-(b/|v3|)

                                                                                N3=+/-(c/|v3|).