Find the Cartesian equations of the line passing through A(3, 2, 1) and B(1, 3, 1). - Mathematics and Statistics

Sum

Find the Cartesian equations of the line passing through A(3, 2, 1) and B(1, 3, 1).

Solution

The direction ratios of the line AB are 3 – 1, 2 – 3, 1 – 1 i.e. 2, – 1, 0.
The parametric equations of the line passing through (x1, y1, z1) and having direction ratios a, b, c are
x = x1 + aλ, y = y1 + bλ, z = z1 + cλ
∴ the parametric equations of the line passing through (3, 2, 1) and having direction ratios 2, –1, 0 are
x = 3 + 2λ, y = 2 - λ, z = 1 + 0(λ)

∴ x – 3 = 2λ, y - 2 = -λ, z = 1

∴ (x - 3)/(2) = (y - 2)/(-1) = λ, z = 1

∴ the cartesian equations of the required line are

(x - 3)/(2) = (y - 2)/(-1), z = 1.

Concept: Vector and Cartesian Equations of a Line
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Balbharati Mathematics and Statistics 1 (Arts and Science) 12th Standard HSC Maharashtra State Board
Chapter 6 Line and Plane
Miscellaneous Exercise 6 A | Q 7 | Page 208