Mathematics Part-II

Book: Mathematics Part-II

Chapter: 11. Three Dimensional Geometry

Subject: Maths - Class 12th

Q. No. 5 of Miscellaneous Exercise

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5

If the coordinates of the points A, B, C, D be (1, 2, 3), (4, 5, 7), (–4, 3, –6) and (2, 9, 2) respectively, then find the angle between the lines AB and CD.

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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Chapter Exercises

More Exercise Questions

6

If the lines and are perpendicular, find the value of k.