Compute the orthogonal projection of v = 3 onto the line L through -2 and the origin. projr (7) =

Q: The vector z = (2 + 2i) ( -V3 + i) lies in * the

A: The vector equation is z=2+2i-13+i.

Q: Find a linear mapping G that maps [0, 1]×[0, 1] to the parallelogram in the xy-plane spanned by the…

A: A linear mapping G that maps [0, 1]×[0, 1] to the parallelogram in the xy-plane spanned by the…

Q: 1 Suppose a line passes through the point (1, 1 and parallel to the 2' 3 plane x + y + z = 0. Then…

A: The direction vector of the normal to the plane is (1,1,1) Given that the line is parallel to the…

Q: The image of (-2 , 5) under reflection y = -x followed by translation with translation vector (-3 ,…

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Q: The vector projection of M = 2ax + 3ay + 2az onto P = 3ax + 2ay + 3az is

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Q: Compute the orthogonal projection of 7 = proj,(v) = 4 [1] onto the line L through -4 and the origin.

A: Given:    Data is given

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

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Q: Compute the orthogonal projection of u onto 7. Use the square root symbol 'V' where needed to give…

A: Orthogonal projection

Q: write the equation of the plane with normal vector n passing through the given point in the scalar…

A: We have, Equation of plane through P0 =(x0, y0, z0) with normal vector n = <a, b, c> Vector…

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: Compute the orthogonal  projection of v = [ -3, -3 ] onto the line L through [ 2, -2 ] and the…

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Q: Verify the orthogonality p

A: answer is in next step

Q: Find the vector projection of b = 6î + 3ĵ + 2k onto å = î – 2ĵ – 2k.

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

A: Here we use for product to find he projection.

Q: as a linear combination of x = 7 4 and y = -3 Express the vector u -2

A: NOTE: Refresh your page if you can't see any equations. . write both vectors x and y in the matrix…

Q: Determine the Eq.  of plane (M) pass through points A(0,2,0), B(1,1,1), C(-1,0,2)

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Q: 1 Compute the orthogonal projection of v = onto the line L through -6 and the origin. 2 projz (7) 2.

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Q: Determine the shortest distance from the point (3, 4, 5) to the line through the origin parallel to…

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Q: 3) Write down the equation of line in a vector parametric form, scalar parametric form and standard…

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Q: Compute the orthogonal projection of = 3 onto the line L through -2 and the origin 2 proj, (v) =

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Q: -11 and ỹ = Express the vector u as a linear combination of x 28 x+ y.

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Q: 1. Show that the following vectors are linearly dependent. Uz = U3= %3D -2 3.

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Q: Consider the vectors x1 = (8, 6)T and x2 = (4, −1)T in R2. Let x3 = x1 + x2. Determine the length of…

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Q: 8. Find the scalar equation of the line passing through the point (1, 5) that has a normal vector…

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Q: Find the moment vector m and m of p = [2,3,0] about Q: (2, 1, 0) acting on a line through A: (0, 3,…

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Q: Compute the orthogonal projection of v = [-6   5   1 ]   Onto the line L through [ -2   6   -7] and…

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Q: a) Prove that ||u + v|| = ||u - v|| if and only if u and v are orthogonal, (b) Draw a diagram…

A: a) Suppose u,v are orthogonal. Now…

Q: Defined byT (x, y, z) = (y+2z, –2x+y+2z, –3x– y+52), is diagonalizable.

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Q: 21. Apply the conjugate-gradient method to the problem Ax = b, where 1 A = 1 1 %3D and b = 1 Verify…

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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: Find the equations of the tanget plane and normal line to the graph of In(2?)x-을=3y3-VE at the point…

A: Equation of tangent plane f(x, y, z) = k at x0, y0, z0 is, fxx0, y0, z0x-x0+fyx0, y0, z0y-y0+fzx0,…

Q: Compute the orthogonal projection of i = onto the line L through and the origin. proj, (1) =

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Q: Region A is formed by bounding the lines y= T, y = 6, and the y-axis. Determine which pair %3D of…

A: Region A is formed by bounding the lines y=x, y=6 and y-axis. We have to determine which pair of…

Q: Find the scalar and vector projections of d = (4, 2, –5) on b = (3, –1, 6).

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Q: 1. Determine if the vectors e2t and e-t are linearly inde- e2t e-t pendent/dependent.

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Q: Find an equation of the plane containing the point P(2,1, –1) and having the normal vector N = -î+3…

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Q: 2 3. Show that that the vector u =|-5 is a linear combination of the vectors vi = -4 and vz = 3.

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Q: Compute the orthogonal projection of i = 1 onto the line L through 4 and the origin. projz (5) =

A: Vector projection

Q: Find the particular number of orthogonal transectories of x2+cy2=1 passing through the point (2,1)

A: Given equation is x2+cy2=1........1. We have to find the particular number of orthogonal…

Q: If u = (3, −1, 4) and v = (−2, 3, 5), the scalar projection of y onto v is:

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

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Q: Q3/ Show that the vectors (2i + 3j + 6k), (3i – 6j + 2k)and (6i + 2j + 3k) Are mutually…

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Q: 3. Show that that the vector u = -5 is a linear combination of the vectors vị = 3 U2 = and v3 %3D

A: Given vectors are u=   2-5  3, v1=  1-3  2, v2=  2-4-1 and v3=  1-5  7   To show that u is a linear…

Q: Find the general equation of the plane passing through P(−1, 3, −2) and having n = (−2, 1, −1) as a…

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Q: Find a linear mapping G that maps [0, 1] x [0, 1] to the parallelogram in the xy-plane spanned by…

A: Given: The maps [0, 1] x [0, 1] to the parallelogram in the XY-plane spanned by the vectors (2, 3)…

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

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Q: 1. Show that the vectors u̟ and uz parallel to lines L1 and L2 respectively, are orthogonal. L1: x =…

A: The given equations of lines are: L1:x=5-2t, y=-7+t, z=6+4t and L2:x=2+3t, y=5+2t, z=1+t Rewriting…

Q: Find the orthogonal projection of the vector b =-1 on Nul(A), where -2 -2 3 -10 A = 1 -1 2 3 1 -3 3…

A: For the solution follow the next steps.

Q: Let

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Q: 4. Show that u and v are orthogonal if and only if ||u + v||2 = ||u||2 + ||v||2. (Please avoid an…

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