• Direction cosines of a vector V = ai + bj + ck are (a/|V|, b/|V|, c/|V|), where |V| = √(a²+b²+c²).
• |V| = √(3² + (–2)² + 6²) = √(9+4+36) = √49 = 7.
• Direction cosines = (3/7, –2/7, 6/7).
• Distractor logic: (B) has every sign flipped (would be the direction cosines of the opposite vector –3i+2j–6k); (C) and (D) invert numerator/denominator, a common slip when the magnitude is divided into 1 instead of into each component.
• Final Answer: (A) [3/7, –2/7, 6/7]
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