The vector equations of two lines are:r1= ai + (1 + a)j + (1 − a)kr2 = (2 + 2b)i + (3 + b)j + (−1 + b)kFind the values of a and b when the lines intersect, and hence writedown the (x, y, z) coordinates of the point of intersection

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter1: Vectors
Section: Chapter Questions
Problem 2RQ: 2. If , and the vector is drawn with its tail at the point, find the coordinates of the point at the...
Question

The vector equations of two lines are:
r1= ai + (1 + a)j + (1 − a)k
r2 = (2 + 2b)i + (3 + b)j + (−1 + b)k
Find the values of a and b when the lines intersect, and hence write
down the (x, y, z) coordinates of the point of intersection

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