Let y = proj₁y = 3 -2 and u = -3 (a) Find the orthogonal projection of y onto u. 2 1 = (b) Compute the distance d from y to the line through u and the origin. d

Q: Let L be the line through the point Q = (-2, 9, -4) and direction vector -[-1, 2, -2]T. Find the two…

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Q: Let T: R2 R2 be a reflection in the line y = x. Find the image of each vector. (a) (3, 1)

A: (a)  (1, 3) (b)  (-1, 0) (c)  (0, -a) (d)  (b, 0) (e)  (-d, c) (f)  (g, -f)

Q: Let L. be the line passing through the point P=(5, 1, 1) with direction vector [-1,5, -2], and let T…

A: Solution :

Q: Compute the orthogonal projection of v= 7 onto the line through 4 2 and the origin.

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Q: Let P be the point (1, 1, 4). Find the parametric equations of the line through P and parallel to…

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Q: 5. a) What is the orthogonal projection ŷ, of y = 1 = ( ² ) U = and the origin? -3 9 onto the line…

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Q: Compute the orthogonal projection of v = proj, (v) = -5 onto the line L through -4 and the origin. 6…

A: Introduction:  The vector projection of a vector a on (or onto) a nonzero vector b, sometimes…

Q: Let P(3,-1,4) and Q(10, 13,9) u = (2,5, -1) and v= (7,-1,2) l be the line through P along direction…

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Q: Let L be the line through the point Q = (- 6, - 9, - 10) and direction vector d = [- 1, - 2, - 2]^T.…

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Q: The vector parametric equation for the line through the points (-3, 5, −4) and (5, −5, 0) is L(t) =

A: The given points are -3, 5, -4 and 5, -5, 0. We have to find a parametric equation.

Q: Determine vector and parametric equations for the line in R that passes through the points A(1,0, 1,…

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Q: -2 12. Calculate an orthogonal projection of u onto v if u = 2 ,v = 2 3

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Q: Find the orthogonal projection of y = 8. 4 on W (1)-8} Span

A: The given problem is to find the orthogonal projection of y on the W is span of 2 vectors.

Q: Let L. be the line passing through the point P-(4, -3, 1) with direction vector a-[-4, 1, 1], and…

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Q: Give a vector parametric equation for the line through the point (4, 2) that is perpendicular to the…

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Q: Let a, b and c be the first three non-zero digits of your Banner ID number and consider the points P…

A: Due to Bartleby answering guidelines I have solved only first three Subparts of the given question…

Q: Find vectors u and v such that the parametric equation of the line y= mx + b can be expressed as…

A: Given that  equation of the line is  y= mx + b…