Find the scalar and vector projections of b onto a. a = {1,4} b = {2,3}

Q: Let a = (-3, –4, –4) and b = (2, 2, 4) . Find scalars s and t so that sa + tb = (20, 4, 32) %3D %3D

A: We have to find the values of scalers s and t for a=-3,-4,-4 and b=2,2,4.

Q: Let a = (-10, –10, 10) and b = (8, –4, –4) be vectors. (A) Find the scalar projection of b onto a.…

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Q: Find the scalar and vector projections of b onto a. a=, b=

A: Given: a=<-5, 12> b=<4, 6>

Q: The projection of the vector 5î + 5ĵ – 5k onto the vector –4î + 2ĵ – 4k. | |

A: We have to find out

Q: Consider the vectors u = (-2, 1, –3) and i = (1, –2, – 1). Find the angle between u and ū. (b) Find…

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Q: The orthogonal projection of the vector u=(-1,-2) on a=(-2,3) is 8 12 а) 13 13 13 b) 8 13 12 4 c) 13…

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Q: Find the scalar and vector projections of b onto a. a = (-3, -6, 2), b= (3, 2, 1) -꼭 19 compab = 7…

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Q: Find the scalar and vector projections of b onto a. a = (-1, 4, 8), b = (14, 1, 2) 6 scalar…

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Q: Let a = (5, 3, 8) and b = (-3, –2,–7) be vectors. (A) Find the scalar projection of b onto a. Scalar…

A: Given data is: a=5,3,8 and b=-3,-2,-7

Q: Find the scalar and vector projections of b onto a. a = (1, 5), b = (-6, 1) comp,b proj b

A: a = 1i + 5j  b =  -6i + 1j

Q: (a) Determine whether the vectors vi = (1,1,2), v2 =(1,0,1) and v3 = (2,1,3) span the vector %3D %3D…

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Q: Find the scalar and vector projections of b onto a. a = ⟨-3,4⟩, b = ⟨7,9⟩ scalar projection of b…

A: The given points in vector form, a→=-3i^+4j^b→=7i^+9j^ The Scalar Projection of b onto a, is given…

Q: Find an orthogonal basis for A1, A2, A3 (i.e., find 3 mutually perpendicular vectors u1, u2, u3 with…

A: The solution are next step

Q: Find the projection of the vector a = (2, 5, 1) on the vector b = (1, 1, 3) O a. (10/11)(ax + 3ay +…

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Q: Find the scalar and vector projections of b onto a. a = 4, 7, −4 b = 4, −1, 1

A: The scalar projection of b→ on to a→ is given by: a→·b→a→ And, the vector projection of b→ on to a→…

Q: Let a = (-1,6, –5) and b = (-7,3, –1) be vectors. (A) Find the scalar projection of b onto a. Scalar…

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Q: Let u = (2, 1, 5) and v = (3, 4, 2). Find the scalar and vector projections: comp,u, uv

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Q: Find the scalar and vector projections of b onto a. a = b =

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Q: 24. If A and B are nonzero vectors, prove that the vector A- cB is orthogonal to B if e= A· B/|B.…

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Q: Let a = (1,2,3), b = (1,0, –1) and c = (2, 1, 3). (a) Verify that a · (2 b+c) = 2 (a · b) + (a · c).…

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Q: Find the scalar and vector projections of b onto a. a = (1,6), b = (-7, 1) compab = projb =

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Q: Find the scalar and vector projections of b onto a. a = (-3, 4), b = (7, 9) scalar projection of b…

A: Give a→=<-3,4>, b→=<7,9>We find the scalar and vector projection of b→ and a→

Q: 5. Show that the vector ortha(b) = b – proja(b) is orthogonal to a. This vector is called an…

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Q: orthonormal 3D vectors

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Q: Find the scalar and vector projections of b onto a. a = (4,7,-4) b =(4,-1, 1)

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Q: -1 the vectors -3 -2 and 20 linearly independent? 4. noose ey are linearly dependent, find scalars…

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Q: (g) Can a basis for R' contain 9 vectors? Explain why or why not. 1 (h) Normalize the vector v = 1 1

A: Result: If dimension of a vector space V is n then the every basis of V contains exactly n elements.…

Q: 5) Find the scalar and vector projections for b = (-3,1,7) onto a = (0,-2, 2).

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Q: Find the scalar projection of A = 2.50 ax + 1.21 ay + 5.32 az perpendicular to the plane containing…

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Q: a) Show that the set of vectors are orthogonal vectors in R3 U1 = (1, -2, 3), u2 = (1, 2, 1) and u3…

A: Definition: Two vectors u and v are called orthogonal (or perpendicular) if (u, v) = 0.    A set of…

Q: Find the scalar and vector projections of b onto a. = (3, –6, –2), b = (3, 3, 2) a

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Q: Construct a matrix to scale by a factor of 5 abou the plane through the origin perpendicular to the…

A: Given: To construct a matrix to scale by a factor of 5 is given as,  is the vector .

Q: 3- Suppose that A = {x1 = (2,1,3), x2 = (2,0,1), x3 = (3,0,4)} then [A] = R³, then the scalars we…

A: We will use the fact that any arbitrary vector in  R3 is of the form (x,y,z).

Q: Consider the points C(3,-2,0), D(-1,5,-1). Let b be the vector with representation CD. Write b in…

A: Ans:

Q: Find a subset of the vectors that forms a basis of their span: (i) vi = (-1,1, -2,1), v2 = (2,-2,…

A: For (i), Notice that v2=2, -2, 4, -2=-2-1, 1, -2, 1=-2v1. So, the subset of the vectors that form a…

Q: Consider the following vectors: 2 -3 u = 2 v = w = -6 3 a. Do these vectors form an orthogonal set?…

A: For linearly independent vector set orthogonal is equal to orthonormal vector. Please find the…

Q: Let u = (-3, -1, 3) and : = (3, 1, 2). Find the vector component of u orthogonal to a. a 3D

A: Since you have asked multiple questions in single request  so we  will be answering only first…

Q: 2. Consider the vectors v1= (-1, 2, 1), v2= (-2, 4, 2), and v3= (-3,6, 3). (a) Are the vectors…

A: As per our company guidelines we are supposed to answer only the first 3 subparts. Kindly re post…

Q: Let a = (8, -6, 7) and b = (4, –10, 4) be vectors. (A) Find the scalar projection of b onto a.…

A: Givena=8,-6,7b=(4,-10,4,)

Q: Find the scalar and vector projections of b onto a. a = (-3, -6, 2), b= (3, 2, 1) compab projb=

A: Given a→=−3,−6,2 and b→=3,2,1 We have to find the scalar and vector projection of b→ onto a→. The…

Q: Find the scalar and vector projections of b onto a. a = 3i − j + 4k,    b = j + (1/2)k   compab =…

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Q: Find a real number k such that the following three vectors in Rª are not linearly independent. (1,0,…

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Q: nd scalars a, b and c such that a(2,0,1) +b (1,3,2)+c(1,0,1)=(7,3,4)

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Q: Let a = (-6, 2, 7) and b = (10, –1,6) be vectors. (A) Find the scalar projection of b onto a. Scalar…

A: Scaler projection of b onto a = b→.a→a→

Q: 3. Find the vector component of u along a and the vector component of u orthogonal to a for the…

A: Given that the vector u=2, 0, 1 and the vector a=1, 2, 3. We have to find the vector component of u…

Q: Let x, y, and z be vectors in Cn and let α and β becomplex scalars. Show thatz, αx + βy} = α z, x} +…

A: Given: z,αx+βy=αz,x+βz,y

Q: Find the scalar and vector projections of b onto a. (4, 7, -4) ь 3 (3, -1, 1) a

A: a=4, 7, -4, b=3, -1, 1 1. Scalar projection of b onto a is Proj ba. Proj ba=b·aa          =3, -1,…