(i) Compute the vector projection of u onto v, proj u , where V u = (3, 3) & v= (2, 0). (ii) What is the length of proj u ? V

Q: Find a non-zero vector 7 perpendicular to the vector u 12 [3]. -6

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Q: Compute the angle between the vectors u = [2, 1, -2] and v = [1, 1, 1].

A: To find out the angle between two vector use the formula. First find dot product of these two…

Q: 1 of the unit vector u =- +!= j. 2/2 2/2

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Q: Verify the Cauchy-Schwarz Inequality for the vectors.u = (1, 1, −2), v = (1, −3, −2)

A: By Cauchy-Schwarz Inequality for the vectors, we have

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Q: 8. Let C = 2 c=(; 1) - (;) ()- and b = Find a 2-vector z such that Cz = b.

A: we have  C=112-1b=11   we have to find a 2-vector such that  Cz=b

Q: Find a unit vector orthogonal to both u and v.u = (2, −1, 3) v = (1, 0, −2)

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Q: Prove that u is orthogonal to v - proju(v) for all vectors u and v in Rn, where u ≠ 0.

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Q: u.v<0, u.w < 0 ,w .u < 0 ?

A: Given data:     The given first vector is: u. The given second vector is: v. The given third vector…

Q: 4. If the projections of vector a on x,y and z −axes are 2,1,2 units respectively, and the angle at…

A: To calculate the angle we use dot product of two vectors given by Taking two vectors as U&amp;V…

Q: · Let 2 be the separation vector from a fixed point (x', y', z') to the point (x, y, z), and let z…

A: Since r is the separation vector from the point x',y',z' to the point x,y,z and the difference…

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Q: Find the projection of u onto v and find the vector component of u orthogonal to v. u = ⟨9, 7⟩, v =…

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Q: Find a non-zero vector v perpendicular to the vector u = [ -1 ]                          [ 8 ]

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Q: Find a unit vector in the xy-plane that is orthogonal to

A: Here given vector as a=123 Consider a vector as b=25-150 Now find the dot product of vector b to…

Q: Determine all vectors v that are orthogonal to u.u = (2, −1, 1, 2)

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Q: find a vector parametrization for the line with thegiven description. Passes through P = (4, 0, 8),…

A: The parametric equation of a line in vector for is given by the expression r→=u→+tv→. Here u→ is the…

Q: The scalar projection of vector A onto another vector B will be the negative of that scalar…

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Q: Determine all vectors v that are orthogonal to u.u = (0, 1, 2, −1)

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Q: Find a unit vector orthogonal to both u and v.u = (−4, 3, −2) v = (−1, 1, 0)

A: Given u→=(-4,3,-2)v→=(-1,1,0) unit vector orthogonal to both u and v is gruen by     u→×v→‖u→×v→‖

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A: Here we have to find the vector of length =2 and  orthogonal to the plane 3x - 4z = 5 Let the vector…

Q: Find the projection of u onto v and find the vector component of u orthogonal to v. u = ⟨8, 2, 0⟩,…

A: Consider the given vector u=8,2,0 and v=2,1,-1

Q: Find two vectors of norm 1 that are orthogonal to the vectors u = and v =

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Q: How do you find out the projection of a vector u on a vector w

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Q: orthogonal to the vector y = (2)? You may want to go through the proof of When is the vector x =…

A: Here,        x = (3, 4)T       y = (-4, y2)T x and y is orthogonal if xTy = 0.

Q: Thẻ nòrmal vector to the plane 3x + 4y – 5z – 6 = 0 is A 3i+ 4j – Sk B 3i + 4j + Sk C 3i+ 4j – 6k D…

A: It is normal vector form.

Q: Find the vector projy u. u = 3 i - j+ 3 k, V = 2 i+ j+ 2 k

A: We want to have projection vector. Projection of vector u on v is given by u.vvv⏞

Q: Verify the Cauchy-Schwarz Inequality for the vectors.u = (6, 8), v = (3, −2)

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Q: Verify the Cauchy-Schwarz Inequality for the vectors.u = (1, −1, 0), v = (0, 1, −1)

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Q: Determine all vectors v that are orthogonal to u.u = (4, −1, 0)

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Q: Let v =5j and let u be a vector with length 3 that starts at the origin and rotates in the xy-plane.…

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Q: How does translation T along vector AB affect the points in the plane?

A: Some information in the question is missing.

Q: Describe all vectors v that are orthogonal to u

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Q: Let a be the angle between the vectors u=(-3,4,0) and v=(-4,3,0). Then

A: Given, the vectors u=(-3, 4, 0), and v = (-4, 3, 0).

Q: Compute the angle between the vectors u = [2,1, -2] and v = [1, 1,1].

A: Given: u=21-2   and   v=111 Formula Used: cosθ=u.vuv

Q: Evaluate The Work Done By The Force Vector, F= (6x^2+3y)I – 15yzj + 10x^2zk From (0,0,0) To (1,1,1)…

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Q: Prove: For nonzero vectors ū,vER, if (dot product) ū-v=0, then ū & v are linearly independent. Hint:…

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Q: Determine all vectors v that are orthogonal to u.u = (0, 5)

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Q: Evaluate The Work Done By The Force Vector, F= (6x^2+3y)I – 15yzj + 10x^2zk From (0,0,0) To (1,1,1)…

A: The line integral ∫CF·dr involves the integration over a specific path. In this problem, the…

Q: 2. Can three vectors in the xy plane R2, have u v < 0, v w < 0, w u<0?

A: Given that, u, v and w are vectors in XY plane. The dot product of vectors is defined as, if u = a1…

Q: Is it true or false that the vector u (3, 3, –3) is a normal vector to the plane -x – y + z + 3 = 0…

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Q: ) orthogonal to the vector y = (2)? You may want to go through the proof of When is the vector x =…

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Q: Let f(x, y) = 5y² ln(4x). Then Duf(1,4) in the direction of the vector (-2, –2) is

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Q: 4. A unit vector orthogonal to A and whose representations are parallel to the yz-plane.

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Q: Let u = -2i + 3j, v = 6i - j, w = -3i.Find specified vector ||u + v ||2 - ||u - v||2 or scaler.

A: Given vectors are  u = -2i + 3j, v = 6i - j, w = -3i.

Q: -2 - are the vectors U, = %3D Ug = %3D in M22 are lineor ly depon dent linearly in dependet.

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Q: ind a vector orthogonal to both u and j+k. u=2i-j+3k

A: we have been given two vectors,  u = j+k. v=2i-j+3k   the unit vector that is orthogonal to both…

Q: Find a nonzero vector parallel to the line of intersection of the two planes 4y – 3x +3z = -2 and z…

A: Answer

Q: Find a nonzero vector parallel to the line of intersection of the two planes 5z – (3x+3y) : 2 and 2x…

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