Verify that fu,,u2} is an orthogonal set, and then find the orthogonal projection of y onto Span(u,,u2}. - 6 y = u1 = u2 = - 1 To verify that {u1.42} is an orthogonal set, find u, • u2. u1 •u2 = (Simplify your answer.) The projection of y onto Span{u,,u2} is (Simplify your answers.)

Q: What is translation that map each preimage to its image in (a) coordinate notations and (b) as a…

A: The image before dilation is referred to as the pre-image. After dilating with a dilation factor,…

Q: Find the distance between the given pair of points in Exercises 25–28. 25. (−1, 4, −3) and (−4, 3,…

A: To find the distance between the pair of points given: d=x2-x12+y2-y12 in a two coordinate plane.…

Q: 7. Let ui (1,4, 2), из (0, 3, 1), из — (1,1, 1), ид — (1, 3, —3) represent four 6. points in the…

A: Since part (i) is very lengthy, we solve first part only. For other part please resubmit.

Q: Suppose ū = (3, 3, 5) and ī = (-4, 4, 2). Then: 1. The projection of u along v is

A:

Q: Compute the orthogonal projection of 7 = projz (7) = onto the line L through and the origin.

A: The given data is: v→=-69 To compute the orthogonal projection of v→=-69 onto the line L through -76…

Q: 1. Get center point of homo geneu us plane limited by 9) y =4- x2 and x axis

A: Hi! Thank you for the question, As per the honor code, we are allowed to answer one question at a…

Q: the distance between u = (-1,2,5) and v = (3,0,1)

A:

Q: What is the point of intersection of the following line and plane: line: 7 = [3, 1, 2] + t [1, - 4,…

A: Given  r⇀=3,1,2+t1,-4,-8& plane π=4x+2y-z-8=0 To find point of intersection:

Q: 2. Determine whether a translation maps quadrilateral LMNP onto quadrilateral L'MNP. If so, find the…

A: We have to find the translation which maps quadrilateral LMNP onto quadrilateral L'M'N'P'.  The…

Q: If vector u =(7,6) and v= (-3,5) then  Find u•v

A: Given ,  If vector  u = (7,6)  v = (-3,5)  We have to find dot product u•v

Q: Let a = (– 5, 5, – 3) and b = (2, 1, 3). Find the projection of b onto a. proja

A: Projection b onto a is b→.a→a→2.a→

Q: Verify that {uq.u2} is an orthogonal set, and then find the orthogonal projection of y onto…

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Q: 9. Find orthogonal projection of u=(-1, 2, 5) in the direction of v=(3, 1, -2).

A:

Q: Find the distance from P(1, 5, −2) to the plane passing through Q(5, −4, 3), R(4, 1, 1) and S(−2, 4,…

A: To Find: Find the distance from P1,5,-2 to the plane passing through Q5,-4,3R4,1,1 and S-2,4,2.…

Q: Describe the translation that maps each preimage to its image in A coordinate notations and B as a…

A:

Q: Find the projection of u onto v if, u= (4, 2), v = (5, -2).

A: Given, Formula for the projection of u onto v is given by

Q: show that the pants AC1,1,4), B(2,2,2), c(o,l,5) and D(1,0,5) coplanear (in the are Same plane).

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: What are the coordinate planes in three-dimensional space? How are they drawn?

A: The Cartesian coordinate system is used to describe three-dimensional space which consists of an…

Q: Find a plane containing the point (- 5, – 5, 2) and the line r (t) = (1, – 2, 1) + t(4, 7, 5).

A: Given that the required plane passes through the point P=(-5,-5,2) and required plane contains the…

Q: 9. Let A=span{v = (-1,–1,2), i = Projau. (2,3,0)} and w (1,2, 3). Find

A:

Q: find the projection of u along v u = (2, 5), v = (1, 1)

A: u=2,5 and v=1,1

Q: Define spanning set. Determine whether the vectors u = (1,2,0), 2 = (-1,1,2) and uz = (3,0,–4) span…

A: We need to define spanning set and to determine if the given vectors span R3  This can be done as…

Q: Prove that a projective plane (P,L,I) has the property that every line contains at least three…

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Q: Find orthogonal projection of u=(-1, 2, 5) in the direction of v=(3, 1, -2).

A: find the orthogonal projection of u=-1,2,5 in the direction of vector v=3,1,2 it is known that…

Q: Sketch the set X = [1, 3] × [1, 2] on the plane R . On separate drawings, shade in X ∩([0,2]×[0,3]).…

A: Sketch the product X = [1, 3] × [1, 2] on ℝ.

Q: Find the projection of u along v. u =〈2, -3〉, v =〈1, 2〉

A: Given: u =〈2, -3〉, v =〈1, 2〉 To find the projection of u along v

Q: Show that the vectors v = (0, 3, 1, -1); v, =(6, 0, 5, 1); v, = (4, -7, 1, 3) form a linearly…

A: Solution:

Q: Find the general quation of plane containing the point P(-1,3,3), and perpendicular to the line…

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Q: A plane through the three points P = (4, -3, 5), Q = (-2, -3, 5), and R= (-2, 3, -3) is described by…

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Q: Find the projection of u onto v if u= (5,-3), v = (-1,4).

A:

Q: ortho ne plane through the points -1,0,0), (0, –1, –2), 2, 3, 4) is

A: Please refer to the image below

Q: Suppose {u1,u2,...,un} is a set of vectors that span V, and that {v1,v2,...,vk} is an independent…

A:

Q: Compute the orthogonal projection of u' onto v. Use the square root symbol 'V where needed to give…

A: We need to find orthogonal projection of u onto v.

Q: 10- -10 -8 -6 4 4 6 8 10 -10- 2. 2.

A: Given query is to find distance between two points G and N.

Q: 10. If 3(a, 3, 2)-2(3, b, b) = (-3, 1, -2), determine a and b. Describe the set spanned by the…

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Q: 1 Find the plane through the points A(1,2,-), B(4,2,-2) and C(2,3,4)?

A: We are given the points : A(1,2,14) , B(4,2-2) and C( 2,3,4) Equation of a plane passing through…

Q: Write v as a linear combination of u,, u2, and uz, if possible. (If not possible, enter IMPOSSIBLE.)…

A:

Q: Verify that (u,,u2} is an orthogonal set, and then find the orthogonal projection of y onto Span…

A:

Q: 4. Describe in words the translation of X represented by a translation vector of .

A: Translation vector is a type of geometric transformation. A translation vector moves or translates a…

Q: The point (-1, 0, 3) is located on the: O xy plane O xz plane O yz plane O all of the above

A: Applying coordinate geometry we have

Q: Find orthogonal projection of v=(3, 1, -2) in the direction of u=(-1, 2, 5).

A:

Q: Let u = (a, b, c) and v = (7,8, 9). If u is parallel to (1,0, –1) and the projection of u along v is…

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Q: Find a plane containing the point ( - 5, - 5, 2) and the line r(t) = (1, - 2, 1) + t(4, 7, 5).

A: First you will find the normal vector to the plane and then find the value of the constant d

Q: Find three numbers a1, a2, az to normalize the orthogonal set 1 -2 a1 , a2 , аз 1 in R3. , az = = Ip

A: Here, a1 , a2 and a3 are unit vectors . w1 = (1,-1,3)  w2 = (-2,1,1)  w3 = (4,7,1)

Q: (5) Let 8. u = 6. --(:)- and y = 1 What is the orthogonal projection of y to the line through u and…

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Q: Verify that (u.u2) is an orthogonal set, and then find the orthogonal projection of y onto Span (u,…

A: For two vectors to be orthogonal, the dot product should be zero.

Q: What are the projections of the point (3,−2,−7)(3,−2,−7) on the coordinate planes? on the xy plane?…

A: