## Book: Mathematics Part-II

### Chapter: 11. Three Dimensional Geometry

#### Subject: Maths - Class 12th

##### Q. No. 3 of Exercise 11.2

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##### Show that 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).

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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