Homework 1.pdf - Heather Macgregor Assignment Homework 1...

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Heather Macgregor MATH6A-03-S18-Martinez Assignment Homework 1 due 04/18/2018 at 11:30pm PDT 1. (1 pt) Consider the line with these parametric equations: x = - 6 t - 9 y = - 2 t + 6 z = 8 t - 1 . One set of symmetric equations for this line is x + 9 - 6 = y - y 0 b = z - z 0 c , where y 0 = , z 0 = , b = , and c = . Another set of symmetric equations for this line is x 3 = y - y 1 b = z - z 1 c , where y 1 = , z 1 = , b = , and c = . 2. (1 pt) Let a = h 9 , 1 , 9 i and b = h- 5 , 2 , 1 i be vectors. Find the scalars and vectors defined below. Note that these formulas only depend on ˆ a = a k a k , the unit vector in the direction of a . The component of b along a : comp a b = ˆ a · b = The projection of b onto a : (Note: you can write this without square roots.) P a b = ( ˆ a · b ) ˆ a = h , , i The projection of b orthogonal to a : (This is defined in terms of the previous projection.) P a b = b - P a b = h , , i Hint: The meaning of these projections is seen from exam- ples where a = i = h 1 , 0 , 0 i . comp i h 2 , 1 , 5 i = 2, P i h 2 , 1 , 5 i = h 2 , 0 , 0 i , and P i h 2 , 1 , 5 i = h 0 , 1 , 5 i 3. (1 pt) If a = i + 6 j + k and b = i + 14 j + k , find a unit vector with positive first coordinate orthogonal to both a and b .
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