Question:
A line makes angles a, b and g with the positive directions of the coordinate axes. If ai jk /arrowrightnosp/circumflexnosp/circumflexnosp/circumflexnosp (sin )( sin) (sin )22 2 and bi jk /arrowrightnosp/circumflexnosp/circumflexnosp/circumflexnosp then what is ab . equal to?
A line makes angles a, b and g with the positive directions of the coordinate axes. If ai jk /arrowrightnosp/circumflexnosp/circumflexnosp/circumflexnosp (sin )( sin) (sin )22 2 and bi jk /arrowrightnosp/circumflexnosp/circumflexnosp/circumflexnosp then what is ab . equal to?
Options:
- a) -2
- b) -1
- c) 1
- d) 2
- a) -2
- b) -1
- c) 1
- d) 2
correct answer : d)
Explanation:
cos2a + cos2b + cos2g = 1
Þ sin2 a + sin2b + sin2 g = 2
Now, ab
.. = sin2 a + sin2 b + sin2 g = 2
cos2a + cos2b + cos2g = 1
Þ sin2 a + sin2b + sin2 g = 2
Now, ab
.. = sin2 a + sin2 b + sin2 g = 2