Answer :

We know that

Two lines with direction ratios a1, b1, c1 and a2, b2, c2 are parallel if the angle between them is θ = 0°, i. e.



Also, we know that the direction ratios of the line segment joining (x1, y1, z1) and (x2, y2, z2) is taken as x2 – x1, y2 – y1, z2 – z1 (or x1 – x2, y1 – y2, z1 – z2).


The direction ratios of the line through the points (4, 7, 8) and (2, 3, 4) is:


a1 = 2 – 4 = -2, b1 = 3 – 7 = -4, c1 = 4 – 8 = -4


And the direction ratios of the line through the points (– 1, – 2, 1) and (1, 2, 5) is:


a2 = 1 – (-1) = 1 + 1 = 2, b2 = 2 – (-2) = 2 + 2 = 4, c2 = 5 – 1 = 4


Consider



The line through the points (4, 7, 8), (2, 3, 4) is parallel to the line through the points (–1, –2, 1), (1, 2, 5).


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