The direction ratios of two lines are given byp,q,r  and  1qr,1rp,1pq. Ifis the angle between them such that 0≤α<π, then the value of  cosα+cos2α+cos3α+....+cospα⋅cosqα⋅cosrα=

The direction rations of two lines are given as p,q,r  and  1qr,1rp,1pqMultiply the second set of direction rations with pqr, then the direction ratios arep,q,rIt implies that both lines are parallel. Henceα=0°Therefore, the required value is  1+1+1+....+p+q+r times=p+q+r