Given the points A(3,-1,1), B(2,3,4) and C(4,1,1).(a) Find a unit vector that is simultanously orthogonal to both AB' and AC(b) Find an equation of the plane passing through A, B and C.(c) Find the line of intersection of the plane from part b) and the XZ-plane.

Concept: A plane going through three non-collinear points has the following equation: Vectors and…

Answered: Given the points A(3,-1,1), B(2,3,4)…

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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Given the points A(3,-1,1), B(2,3,4) and C(4,1,1). (a) Find a unit vector that is simultanously orthogonal to both AB' and AC (b) Find an equation of the plane passing through A, B and C. (c) Find the line of intersection of the plane from part b) and the XZ-plane.