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University of Toronto Department of Mathematics MAT223H1F Linear Algebra I Midterm Exam II November 24, 2011 C. Anghel, S. Arkhipov, S. Shahroki-Tehrani, S. Uppal Duration: 1 hour 30 minutes Last Name: Given Name: Student Number: Tutorial Group: No calculators or other aids are allowed. FOR MARKER USE ONLY Question Mark 1 /10 2 /10 3 /10 4 /10 5 /10 6 /5 TOTAL /55 1 of 7 DownloaderID 21140 ItemID 7613 Downloader ID: 21140 Downloader ID: 21140 Downloader ID: 21140 Downloader ID: 21140 1140 Item ID: 7613 Downloader ID: 21140 Item ID: 7613 Item ID: 7613 Downloader ID: 21140 Downloader ID: 21140 Item ID: 7613 Item ID: 7613 Downloader ID: 21140 Downloader ID: 21140 Downloader ID: 21140 Downloader ID: 21140 Downloader ID: 21140 Item ID: 7613 Item ID: 7613 Item ID: 7613 Item ID: 7613 Downloader ID: 21140 Item ID: 7613 Item ID: 7613 Downloader ID: 21140 Item ID: 7613
1. Consider the points P = (1 , 2 , 3) and Q = (4 , 5 , 6) in R 3 . [6] (a) Find an equation for the plane that passes through the origin and contains the points P and Q . Express your answer in the form ax + by + cz = d . [2] (b) Find the orthogonal projection of ( 1 , 0 , 8) onto the normal vector to the plane in part (a).

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