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A vector has projections 6, -3, and 2 on the x-, y-, and z-axes respectively. Its direction cosines are:

1. (6)/(5),(-3)/(5),(2)/(5)
2. (6)/(7),(-3)/(7),(2)/(7)
3. (-6)/(7),(-3)/(7),(2)/(7)
4. 6, -3, 2

Correct answer: (6)/(7),(-3)/(7),(2)/(7)

Solution

The correct option represents the direction cosines of the vector, which are calculated by dividing each projection by the vector's magnitude. The magnitude is found using the formula √(6² + (-3)² + 2²) = 7, leading to the direction cosines (6)/(7), (-3)/(7), (2)/(7).

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