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A line passes through A(4, -6, -2) and B(16, -2, 4). The point P(a, b, c), where a, b, c are non-negative integers, on the line AB lies at a distance of 21 units, from the point A. The distance between the points P(a, b, c) and Q(4, -12, 3) is equal to ____

1. 22
2. 21
3. 20
4. 19

Correct answer: 22

Solution

Direction AB=(12,4,6), |AB|=14, unit=(6/7,2/7,3/7). P=A+21*unit=(4+18,-6+6,-2+9)=(22,0,7), non-negative integers. PQ with Q(4,-12,3): sqrt(18^2+12^2+4^2)=sqrt(324+144+16)=sqrt484=22. The stored answer 21 is wrong.

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