Vault Of Euclid

Parametric Equations of Lines in 3D

Vector spaces warmup

Find the (parametric) equation of the line \(L\): (a) through the points \(P(1,3,2)\) and \(Q(2,5, -6)\); (b) containing the point \(P(1,-2,4)\) and perpendicular to the plane \(H\) given by the equation \(3x + 5y +7z = 15\).
analytic-geometrylinear-algebralines-in-3dparametric-equationsdirection-vectornormal-vectorplanesvector-algebrafind-equation

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What this problem tests

Tests the ability to construct a line's equation from geometric descriptions, specifically extracting direction vectors from point pairs and plane equations.

This is a standard introductory problem in multivariable calculus and linear algebra courses, testing the basic geometric interpretation of vectors.

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