# Lines in Space

## •    Equation of lines in space can be uniquely determined in the following two conditions: a)    If the line in space passes through a given point and parallel to a given line. b)    If the line in space passes through two given points.•    In three dimensional geometry the equations of x-axis are y = 0, z = 0; the equations of y-axis are x = 0, z = 0 and the equations of z-axis are y = 0, x = 0.•    Equation of a line in space passing through a given point and parallel to a given vector can be expressed in two forms viz. vector form and Cartesian form.•    The Cartesian form of a line in space passing through a given point (x1, y1, z1) and parallel to a given vector with direction ratios a, b and c is as follows: (x – x1)/a = (y – y1)/b = (z – z1)/c•    Equation of a line passing through two given points (x1, y1, z1) and (x2, y2, z2) in the Cartesian form is as follows: (x – x1)/ (x2 – x1) = (y – y1)/ (y2 – y1) = (z – z1)/ (z2 – z1)Keywords: Equation of a line in space, Equation of a line through a given point and parallel to a given vector, Equation of a line through two given points, Angle between two lines

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• Q1

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• Q2

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• Q3

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• Q4

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• Q5

Find the vector equation of the line through points A (1, 4, –5) and B (1, –1, 7).

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