A line l passing through the origin is perpendicular to the line l1 : (3+t) i^ + (−1+ 2t) j^ + (4+ 2t) k^,−∞

The line l is perpendicular to l1 and l2. Hence the direction ratios of  l are given by the vectori^j^k^122221=− 2i^  +  3j^ − 2k^Let P ≡ (2r, − 3r, 2r)As it lies in l1, we have 2r− 31=−3r+ 12=2r−42Thus we have r=1 and P≡  (2, − 3, 2)A point on l2 is then (3+ 2s,  3 + 2s, 2 + s)(3 + 2s − 2)2 + (3 + 2s + 3)2 + (2 + s− 2)2  = 17⇒  9s2 + 28s + 20 = 0 given s = − 2, − 10/9Thus the points are  (−1,   1, 0) and 79, 79 ,89