Question:
If a line in 3 dimensions makes angles a, b and g with the positive directions of the coordinate axes, then what is cos( a + b) cos (a – b) equal to?
If a line in 3 dimensions makes angles a, b and g with the positive directions of the coordinate axes, then what is cos( a + b) cos (a – b) equal to?
Options:
- a) cos2g
- b) -cos2g
- c) sin2g
- d) -sin2g
- a) cos2g
- b) -cos2g
- c) sin2g
- d) -sin2g
correct answer : b)
Explanation:
We know that cos2a + cos2b + cos2g = 1 …(i)
and cos(a + b) cos (a – b) = cos2a – sin2b
= cos2a + cos2b – 1 = 1 – cos2g – 1 = -cos2g.
We know that cos2a + cos2b + cos2g = 1 …(i)
and cos(a + b) cos (a – b) = cos2a – sin2b
= cos2a + cos2b – 1 = 1 – cos2g – 1 = -cos2g.