Find the cosine of the angle between the vectors P1 (x) = 1 + 2x – x2 and p2 (x) = -2 3x + 2x? %3D - %3D with respect to the standard inner product on P2. O None -10 102 -2 102 -10 84 -9 84

Q: 7. What is the cross product (Ax B) of the given vectors below? A = -4i + 7j B = 3i

A: Answer of mathematics: Given: log3x2=log3(7x-10) Since base of log are same therefore: x2=7x-10…

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A: We have to find the scalar product

Q: H.w: Determine if the two vectors are orthogonal or parallel or not? A= 6i+6k 1- and B=-2i+2j+2k 2-…

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Q: Find the best approximation to z by vectors of the form c,v, + C2V2. 3 1 - 6 2 - 1 V2 = - 3 3 1 The…

A: Solution

Q: Find the Euclidean inner product of the given vectors. 3 4 u = v = (u, v) = Ex: 5

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Q: 3. Find the dot product of the vectors d = (-5, 3) and 7 = (1,7).

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Q: A, B, and C are 3 distinct points with non-zero position vectors a, b, and e respectively. a If a x…

A: Given three distinct points are A, B, C. with position vectors a, b, c respectively.…

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Q: Find the magnitude R and direction 0 of the resultant vectors. 7.0N 5.0N 5.0N 6.0N 2.5N 80 20 30 10…

A: if you find my answer helpful please put thumbs up. thank you. the required solution is given below…

Q: n Let ú and ú be two nonzero vectors in R" for which ú + 2v is orthogonal to ủ – 20. What is the…

A: We have to find the ratio

Q: Find a so that the vectors v=i-aj and w = - 10i+ 7j are orthogonal. a = (Type an integer or a…

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Q: 8. If you know that the vectors a = 4i-j + 2k and b =4i-2j-5k, then the lengthvector %3D a - 2b = A.…

A: To find: The length of the vector a→-2b→. Given: The vectors are a→=4i-j+2k and b→=4i-2j-5k. Concept…

Q: (c) Consider the basis vectors ê1 = * and êz = *. What is the length of the vector V defined as V =…

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Q: Find the cosine of the angle between the vectors PI(x) = 1 + 2x – x and p2 (x) = -2 -x + 3r with…

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Q: 12. Let A = ( d ef g h Find the column vector B such that AB =

A: Let A be a square matrix. Use the following formulae, to obtain the required result.

Q: Find the value of y in ( 3x + 4yi)(6 -7i) = 3 + 5i  A. 1/20 c. 1/10  B. 3/20 d. -1/15   Q2: If…

A: We have to find the value of y.

Q: Find the weighted Euclidean inner product (u, v) = -3v1 u1 – 3vzuz of the given vectors. u = (u, v)…

A: Given u, v=-3v1u1-3v2u2 u=-3-2, v=14

Q: -2 [5a] Find the value of a such that the vectors u =a +4 and v = |2 are orthogonal.

A: Please refer the attached image for complete solution. Given: u = -2a+4   1  & v = 5a 2 0 are…

Q: Find the angle between the following vectors relative to the Euclidean inner product on ℝ2. a.…

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Q: Which of the following is the correct value of the dot product for the vectors: u→=(6,−2,5) and…

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Q: -2 Find Q for the QR factorization of A -5 , given the orthogonal vectors -1 -3 2 -0.89 Vi = -5 , V3…

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Q: Use the triple scalar product to find the value of p that makes the three vectors below coplanar.…

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Q: 14. Find a vector perpendicular to both of the vectors * (ũ + v) and (ũ – v) where ủ = 2i – j + k,…

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Q: Find the cosine of the angle between the vectors P1(x) = 1 + 2x – x² and p2(x) = 2 – 3x – 2x² with…

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Q: Find the cosine of the angle between the vectors P1 (x) = 1 + 2xr – x² and p2 (x) = -2 – 3x + 2x² -…

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Q: 4. ABP is a triangle, M is a point on AP. AB = a, AM = 26, and MP = b. N is the midpoint of BP. C is…

A: Follow the steps.

Q: Express F= 100 N (shown in the figure below) as a Cartesian vector. a) 35.4i – 35.4j+ 86.6k b) 35.4i…

A: Here we have to find the components of 100N on each axis.

Q: A = x1+ y2+ z3 B = x 3+ y 2+ zl For the given vectors A,B, and C and , compute the triple cross…

A: Topic- vector cross product

Q: 10. In the diagram, M is the mid-point of CD, BP:PM = 2:1, AB AD = z. = x, and AC = y and %3D…

A: Given that:                               NOTE: As per our answering guidelines, we can only answer…

Q: Find a so that the vectors v = i- aj and w = - 9i - 8j are orthogonal. (Type an integer or a…

A: As we know that; If two vectors v & w are orthogonal to each other then the dot product or…

Q: The dot product ol tWU veciurs Y1 Y2 and y = Yn in R" is defined by a· j = x1yh + x2y2 +... + x„Yn.…

A: Given: x=8-83 We need to find a vector y such that x.y=0. This can be done as follows:

Q: Find the best approximation to z by vectors of the form c, v, + C, V2. 4 2 -5 1 1 z= 2 3 -1 The best…

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Q: Find the cosine of the angle between the vectors P1(x) = 1 + 2x – x² and p2(x) = -1 – 3x + 2r² with…

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Q: If A= (3/2) i –(½) j + k and B= i+j+2k, what is the value of A x B? Are the vectors orthogonal? O…

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Q: Which of the following vectors form an orthogona EBA • BBR [0] 31 [0 a) b) -2 3 1 [2 [-2] c) 12 d)…

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Q: 1. Perform the stated operations on the vectors u, v and w. u = 3i – k, v=i-j+2k, w = 3j (а) w- v…

A: Using addition & subtraction of vectors. Adding & subtracting same component's.

Q: Which of the following vectors are not orthogonal to the vector i = Check all that apply. 3 0 -2…

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Q: 98 25) Gvon vectors v= 30tj and w=-2i -j. Decompose v into two vectors V, and Vz, where V, is…

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Q: Find the best approximation to z by vectors of the form c, v1 + C2V2. 3 3 6 15 - 1 V2= - 1 z= - 3…

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Q: Find the cosine of the angle between the vectors P1 (x) = 1 + 2r – x² and p2 (x) -2 – x + 3x? %3D…

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Q: Let u = -5i-6j and v = 2i-4j. Decompose u into two vectors u, and u,, where u, is parallel to v and…

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Q: Find the best approximation to z by vectors of the form c,v1 + C2V2. 2 1 - 5 1 - 1 3 - 3 2 1 1 The…

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Q: Find the best approximation to z by vectors of the form c,v, + C2V2. 3 3 6 1 V2 = 1 V1 = - 2 4 3 - 2…

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Q: Let R2 have the inner product (u,v) = 4u, V, + 4u,V2, and let x = (3,1) and y = (4, – 1). a. Find…

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Q: Let W = {[x]∈ R2^ | y > or equal to 0} .             [y] (a) If u and v are vectors in W , is u + v…

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Q: 3. Find the angles between the vectors: a. u = 2i + j, b. u = 2i – 2j + k, v = 3i + 4k v = i + 2j –…

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Q: Find the Euclidean inner product of the given vectors. 4 5 u = 3 v = 1 -4. -2 (u, v) =Ex: 5

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Q: Use the standard inner product on R" to determine if the vectors or functions are orthogonal. 2 -3 1…

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Q: If v = 5i + 6j and w = 10i + 12j, find proj,v. Then decompose v into two vectors v, and v2, where v,…

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Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.