Sum

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.

Concept: Vector and Cartesian Equations of a Line

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