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 A B 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 __________.

(x-4 / 12)=(x+6 / 4)=(z+2 / 6) \ fracx-4(6 / 7)=fracy+6(2 / 7)=fracz+2(3 / 7)=21 \ (21 x (6 / 7)+4, (2 / 7) x 21-6, (3 / 7) x 21-2) \ =(22,0,7)=(a, b, c) \ Therefore sqrt(324+144+16)=22 \

A line passes through A462 and B1624 The point Pa b c w... | (Mathematics)

$\begin{aligned} & \frac{x-4}{12}=\frac{x+6}{4}=\frac{z+2}{6} \\ & \frac{x-4}{\frac{6}{7}}=\frac{y+6}{\frac{2}{7}}=\frac{z+2}{\frac{3}{7}}=21 \\ & \left(21 \times \frac{6}{7}+4, \frac{2}{7} \times 21-6, \frac{3}{7} \times 21-2\right) \\ & =(22,0,7)=(a, b, c) \\ & \therefore \sqrt{324+144+16}=22 \end{aligned}$

Explanation

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