Assignment3_F2019.pdf - Math 1300 Section D01 Assignment 3 Due This assignment covers topics from Units 4 and 5 of the course Please make sure that you

# Assignment3_F2019.pdf - Math 1300 Section D01 Assignment 3...

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Math 1300 Section D01 Assignment 3 Due November 10, 2019 This assignment covers topics from Units 4 and 5 of the course. Please make sure that you answer all questions and submit all pages no later than November 10, 23:59 . Late assignments will not be marked . Submission will be done through Crowdmark as for the two previous assignments. You will receive an email with a link to submit your assignment to Crowdmark. Assignments submitted by email sent to me will not be accepted . 1. Let ~u = (1 , 1 , 1), ~s = (4 , 0 , - 4) and ~w = (2 , 0 , - 2). (a) (3 points) Find a unit vector in the opposite direction of ~u . (b) (2 points) Compute ~u × ~w + ~s · ~u . (c) (2 points) Compute ( ~u × ~w ) · ~u . (d) (2 points) Compute ~s × ~w . 2. (4 points) Determine k to have ~u = (2 k, - 3 , 1) and ~v = ( k, 1 , 2) orthogonal. 3. (5 points) Consider 2 vectors ~u and ~v in R n . Given that || ~u || = 2, || ~v || = 4 and ~u · ~v = 0, find || ~u + ~v || . 4. Let Q (0 , 0 , 0) be a point in R 3 , P 1 : x - y + 2 z = 1 and P 2 : 2 x + y + z = 4 be two planes in R 3 . (a) (4 points) Find the general form of the equation of the plane P 3 through Q that is parallel to P

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