Find the coordinates of the point where the line through (5, 1, 6) and (3, 4, 1) crosses the(a) yz –plane(b) zx –planeAlso, Find the angle which this line makes with these planes?

(a) Direction ratio of given line are (5 – 3, 1 – 4, 6 – 1) = (2, – 3, 5)Hence, equation of line isFor any point on the yz –plane x = 0x = 2r + 5 = 0r = y = – 3() + 1 = z = 5() + 6 = Hence, the coordinates of this point are (0, ).

(b): Direction ratio of given line are (5 – 3, 1 – 4, 6 – 1) = (2, – 3, 5)

Hence, equation of line is

For any point on zx –plane y = 0

y = – 3r + 1 = 0

r =

x = 2() + 5 =

z = 5() + 6 =

Hence, the coordinates of this point are (, 0, ).