alleryThe direction cosines of the line joining (1, 2, 3) and (4, 5, 6) are
A(1, 1, 1)
B(3, 3, 3)
C(1/3, 1/3, 1/3)
D(1/√3, 1/√3, 1/√3)
Answer & Solution
Correct answer: D. (1/√3, 1/√3, 1/√3)
1. The direction vector is (4-1, 5-2, 6-3) = (3, 3, 3).
2. Its magnitude is √(9+9+9) = √27 = 3√3.
3. Divide each component by the magnitude: (3, 3, 3) / (3√3) = (1/√3, 1/√3, 1/√3).
4. So the direction cosines are (1/√3, 1/√3, 1/√3).
_Source: syllabus Maths Part 2 Ch 11 "Three Dimensional Geometry", §11.2.2_
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