Ex 11.1, 1 - Chapter 11 Class 12 Three Dimensional Geometry

Transcript

Ex 11.1, 1 If a line makes angles 90°, 135°, 45° with the x, y and z – axes respectively, find its direction cosines. Direction cosines of a line making angle 𝛼 with x – axis, 𝛽 with y – axis and 𝛾 with z – axis are l, m, n l = cos 𝛼, m = cos 𝛽, n = cos 𝛾 Here, 𝛼 = 90°, 𝛽 = 135°, 𝛾 = 45°, So, direction cosines are l = cos 90° = 0 𝑚 = cos⁡135° = cos(180 – 45°) = –cos 45° = (−1)/√2 𝑛 = cos 45° = 1/√2 Therefore, required direction cosines are 0, ( −𝟏)/√𝟐 , 𝟏/√𝟐 .