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

Q: Let x→=8i→−11j→ and y→=4j→−9k→  be two vectors. Find the value of the scalar product x→⋅y→.

A: We have to find the scalar product

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Q: 4. Find the value of t such that the vectors ~v = h2t + 1,-3,3t - 2i and w = h7,4t +2,2i are…

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Q: The dot product of two vectors Y1 Y2 and j = Yn in R" is defined by a · j = x11 + x2y2 + ...+ x„Yn-…

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A: Suppose, the vector normal to A = 2i - 3j is, N = ai + bj

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A: Here we have to find the value of k such that u=1k3 and v=k2-2-1 in ℝ3 orthogonal.

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Q: (2) Find the real values of a,b.c that make the convolution equal to zero for the vector function…

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Q: 2. Find the value of a for which the vector à = (axy – z³)î + (a – 2)x²j + (1 – a)xz²k have it's…

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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: The dot product of two vectors Xị yi X2 and y y2 Xn Yn in R" is defined by x · ỷ = x1yi + x2y2 + ...…

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Q: Let x,y,z be (non-zero) vectors and suppose that z=4x−4y and w=12x−12y−4z. Are the following…

A: A vector is a span of vectors when the first one can be written as the linear combination of the…

Q: 5. (a) Find two vectors of norm 1 that are orthogonal to the vectors u = (5) and pue (4 E)=

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Q: Find the value of k for which the vectors 4 and 4 k are orthogonal. k =

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Q: d) Prove that ||vxw||²+|v-w[? = ||v||²|w||² for all vectors v, w in R3

A: Prove the following

Q: If u and v are vectors in R^n, and if v≠0 ⃗, then u can be expressed in exactly one way in the form…

A: first draw a figure as below

Q: Find all values of the scalar k for which th e two vectors are orthogonal.

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Q: Given v = - 3i + 5j and w = i+j, a. Find projwv. b. Decompose v into two vectors V1 and V2, where V1…

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Q: Q2] (A) Find the surface area of the portion of the half ball with radius a which cuts off by the…

A: (A)Consider the given information.Let the ball is defined by the sphere and the equation with radius…

Q: For any two vectors ū and i, ||ū + u|| = ||ū|| +||7||-

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Q: Find the possible values of x if vectors are j +2k, v =2i + j –- k and w = xi+j - k coplanar: u = i…

A: Given vectors are u=i-j+2k, v=2i+j-k and w=xi+j-k. To find the possible values of x if vectors are…

Q: Use the vectors a = [-1,0,1], b = [1,-1,5], and č= [0,-1,-2] to prove that a(bxč) # (åxb)xč

A: The answer is given below:

Q: ^2

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Q: Two vectors ñ and m are said to be orthogonal if ñxm3D0

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Find the coordinate vector of p = 2 – 4x relative to the basis B = {q,,q,} for P1 where q1 = 3 + 8x,…

A: Given : We are given a vector,  p = 2-4x  and a basis  B = q1, q2,                 where,  q1= 3+8x…

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: 3. Find two unit vectors that are orthogonal to both j +2k and į -2j + 3k.

A: Solution is here

Q: Q2 Given the vectors r=3i+4j-5k and s=-2J-K, where the xyz coordinate frame is obtained by rotating…

A: The given vectors are:r=3i+4j-5ks=-2j-k We have to find the cross product r×s

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: 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: b/Let u and v be a nonzero vectors in 3- space, and let e be the angle between these vectors when…

A: Let u and v be tthe vectors in 3-spaceThen by Lagrange's identity,we haveu×v2 =u2.v2-(u.v)2…

Q: If U and V are 2 x 1 orthonormal vectors and A = UVT then the trace of A is equal to а. О b. 2 с. -1…

A: We have to find Trace of the Matrix.

Q: 1. Do the vectors 日 span R (over R)? Justify your answer (using methods and results that we have…

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Q: Find all vectors in R2 that are orthogonal to u = (2,1).

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Q: In Rn with inner product{x, y} = xTyderive a formula for the distance between two vectorsx = (x1, .…

A: Take two vectors x and y in an inner product space x=x1,…,xn and y=y1,…,yn then x,y=xTy

Q: Consider the two vectors A = Axî + Ayĵ and B = Bxî + Byĵ. If î · î = ĵ • ĵ = 1 and î · j = ĵ · î =…

A: Note: As per bartleby instruction when more then one question is given only one has to be answered.…

Q: Find the best approximation to z by vectors of the form cv1 + ¢2V2. 3 1 -7 -1 1 V1 V2 -3 3

A: To find  The best approximation to z by vectors of the form c1v1+c2v2.

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

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Q: Find an equation of the plane that passes through the point P(5, 6, 2) and has the vector n = (1,7,…

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Q: For the vectors ü = 2î + 3j – 2k ö = -Sî - 2j – 7k w = 3î + j – 9k the value of [(- ü) x (u – w)].…

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Q: b/Let u and v be a nonzero vectors in 3- space, and let e be the angle between these vectors when…

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Q: One of the following vectors lies in span{ 2+ x +x², 3+x – 2x? } (A) 3 + 2x + 4x² (B) 3 + 2x + 5x?…

A: We have to find

Q: Given v = 6i + 2j and w =i-j, a. Find projwv. b. Decompose v into two vectors v, and V2, where v, is…

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Q: If i • ( or v• (u x w) or w • (u x 7) equal to zero, then the 3, and w vectors u. are coplanar.…

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Q: Show that the vectors (1- i, i) and (2, –1 + i) in C“ are lincarly dependent over C but linear…

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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: One of the following vectors lies in span{ 2+ x + x2, 3+x- 2x2} (A) 2+ 2x + 7x? (B) 2 + 2x + 5x? (C)…

A: The linear span of the given vectors is of the form a(2+x+x2)+b(3+x-2x2)

Q: Find a so that the vectors v = i- aj and w = 7i + 7j are orthogonal. ..... une on integer or o…

A: If two vector orthogonal then dot products will be zero

Magnitude

A vector is an element with both direction and magnitude. A vector is represented using an arrow, where the arrow represents the direction of the vector and its length is represented using the magnitude. The set of vectors in space is known as vector space. The vectors can be added, subtracted, multiplied, and divided in a vector space. The image below shows a vector AB.