A line has direction ratios proportional to (b−c), (c−a), (a−b). Find the sum of its direction cosines.
A line has direction ratios proportional to (b−c), (c−a), (a−b). Find the sum of its direction cosines.
- A. 0
- B. 1
- C. Can't be determined
- D. a + b + c
Answer: A) 0
Explanation: Let DRs be b−c, c−a, a−b. The sum is b−c + c−a + a−b = 0. Since DCs are proportional to DRs, their sum must also be 0 because dividing by a constant magnitude leaves the sum of the numerators as 0.
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