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Question

Find the vector equation of the line passing through the point A(1, 2, –1) and parallel to the line 5x – 25 = 14 – 7y = 35z.

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Solution

The equation of the line 5x − 25 = 14 − 7y = 35z can be re-written as

x-515=y-2-17=z135 x-57=y-2-5=z1

Since the required line is parallel to the given line, so the direction ratios of the required line are proportional to 7, -5, 1.

The vector equation of the required line passing through the point (1, 2, -1) and having direction ratios proportional to 7, -5, 1 is

r=i^+2j^-k^+λ7i^-5j^+k^.

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