Answer :

Angle between the lines with direction ratios a1, b1, c1 and a2, b2, c2 is given by


A line passing through A(x1, y1, z1) and B(x2, y2, z2) has direction ratios (x1 - x2), (y1 - y2), (z1 - z2)


Direction ratios of line joining the points A(1,2,3) and B(4,5,7)


= (4 - 1), (5 - 2), (7 - 3)


= (3,3,4)


a1 = 3, b1 = 3, c1 = 4


Direction ratios of line joining the points C(-4, 3, -6) and B(2,9,2)


= (2 - (-4)), (9 - 3), (2-(-6))


= (6,6,8)


a2 = 6, b2 = 6, c2 = 8


Now,







cosθ = 1


So, θ = 0°


Hence, Angle between the lines AB and CD is 0°.


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