Mathematics Part-II

Book: Mathematics Part-II

Chapter: 11. Three Dimensional Geometry

Subject: Maths - Class 12th

Q. No. 1 of Exercise 11.1

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If a line makes angles 90°, 135°, 45° with the x, y and z-axes respectively, find its direction cosines.

Let the direction cosines of the line making α with x-axis, β – with y axis and γ- with z axis are l, m and n

l = cos α, m = cos β and n = cos γ


Here α = 90°, β = 135° and γ = 45°


So direction cosines are


l = cos 90° = 0


m = cos 135°= cos (180° - 45°) = -cos 45° =


n = cos 45° =


Direction cosines of the line


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