2-2-2 BOOK OF MATHEMATICAL PROBLEMS. 



. a + mz ny b + nx lz c+ly mx 



~>r ~^~' 



obtain them in the form 



x-x Q _y-y Q _z-z 



L M '' N 



1065. A straight line moves parallel to a fixed plane and 

 intersects two fixed straight lines not in the same plane : prove 

 that the locus of a point which divides the part intercepted in 

 a constant ratio is a straight line. 



1066. Determine what straight line is represented by the 

 equations 



a 4- mz ny_b + nx lz_c + ly mx 

 m n n l l m 



Result. The line at oc in the plane 



x (m - n) + y (n - 1) + z (I - m) = ; 

 iinless la + mb + nc = 0, when it is indeterminate. 



1067. The equations 



Ix + my + nz = 0, ax 2 + by 2 + cz* = 0, 



represent two straight lines, the cosine of the angle between 

 which is 



l'(b + c) + ra 2 (c + a) + n*(a + b) 

 JL { (l> - c)" + ... + ... + 2mV(a- b)(a-c)+ ... + ... " 



1068. A straight line moves parallel to the plane y = z, and 

 intersects the curves 



prove that the locus of its trace on the plane of yz is two straight 

 lines at right angles to each other. 



