mat223tut6_1 - Department of Mathematics University of Toronto MAT223H1S Linear Algebra I Winter 2013 Tutorial Problems 6 1(a Find parametric equations

mat223tut6_1 - Department of Mathematics University of...

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Department of Mathematics, University of Toronto MAT223H1S - Linear Algebra I Winter 2013 Tutorial Problems 6 1(a)Find parametric equations of the line passing through (3,-1,-3) that is perpendicular to, and inter-sects, the line passing through (3,-2,4) and (0,3,5). 1(b)Find an equation of the plane through (-2,3,4) and perpendicular to the line through (4,-2,5) and(0,2,4).Note: You can solve these problems using the dot product only - you do not need to use the crossproduct.2.Find the shortest distance from the point (2,3,-1) to the plane 3x-2y+z= 0. What is the pointon the plane closest to (2,3,-1)?3.ConsiderR4together with the standard inner product (i.e. dot produdct). LetX=11andY=11.(a)Show that set setWconsisting of all vectors inR4that are orthogonal to bothXandYis a subspaceofR4.(b)Find a basis forW. 1 of 1

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