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Question
Find the Cartesian equations of the line which passes through points (3, –2, –5) and (3, –2, 6).
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Solution
Let A = (3, –2, –5) and (3, –2, 6)
The direction ratios of the line AB are
3 – 3, – 2 – (– 2), 6 – (– 5) i.e. 0, 0, 11.
The parametric equations of the line passing through (x1, y1, z1) and having direction ratios a, b, c are
x = `x_1 + alambda, y = y_1 blambda, z = z_1 + clambda`
∴ The parametric equations of the line passing through (3, –2, –5) and having direction ratios are 0, 0, 11 are
x = `3 + (0)lambda, y = -2 + 0(lambda), z = -5 + 11lambda`
i.e. x = 3, y = –2, z = 11λ – 5
∴ the cartesian equations of the line are
x = 3, y = –2, z = 11λ – 5, λ is a scalar.
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