Consider the vectors u = (2,0) and v = (-4,4). Sketch the vectors, find the angle between the vectors, and compute the dot product using the definition u•v = u |v| cos €

Q: Find a unit vector that is orthogonal to both u and v. u = (-8, -6, 4) v = (17, -18, –1) V =

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Q: Compute the dot product of the vectors u and v, and find the angle between the vectors. 1= (-…

A: We have to solve given problem:

Q: u and i are vectors of R" such that ||ū|| = 3, |||| = 4 and the angle between them is. Determine the…

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Q: Express the vector in terms of the unit vectors i and j. 2(3, 3) + 3(4, 2)

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Q: Find the area of the parallelogram that has the given vectors as adjacent sides. Use a computer…

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Q: Find a unit vector u in the direction of v. Verify that ||u|| v = (1, -9) U =

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Q: Find the angle 0 between the vectors. u- (3, 2, 0), v = (-2, 3, 4) radians

A: u=3, 2, 0  &  v=-2, 3, 4 Now, u·v=3-2+23+04=0 Now the magnitudes is,…

Q: Find the angle θ between the vectors (a) in radians and (b) in degrees.

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Q: Find a unit vector u in the direction of v. Verify that ||u|| = 1. v = (-6, 6)

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Q: find "a" so that the vectors v=i-ja and w=2i+3j are orthaganal?

A: Given,  v=i-ja and w=2i+3j Two vectors are orthogonal if and only if their dot product is zero

Q: Find a unit vector orthogonal to both u and v. u = -5i – 3j - 2k | V =

A: Two vectors A and B are said to be orthogonal to each other if and only if their dot product is zero…

Q: Find the vectors u + v, u-v, and 5u | u = i + j, v = -j – 2k %3D u + v = u - v = 5u

A: The given vectors are

Q: Find the sine of the angle between vectors u = (-3, 2,6) and v = (3,2,6) by using the cross-product.

A: Given: The vectors u =(-3, 2, 6) and v=(3,2,6) Find : The sine of the angle between the vectors u…

Q: Find the magnitude of the vector and the angle 6,0° <0<360°, that the vector makes with the positive…

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Q: Use the dot product to find the angle between the vectors v =i – 2j + k and w = i+j-2k. For which…

A: First we have to find the angle between the vectors v and w where v=i-2j+k and w=i+j-2k. For this,…

Q: Verify the Pythagorean Theorem for the vectors u and v.u = (4, 1, −5), v = (2, −3, 1)

A: Given   The vector u = (4, 1, −5), v = (2, −3, 1) Pythagorean Theorem for the vectors

Q: The plane contains the point (−2, 3, −1) and is normal to the vector 3i − 2j.

A: Given: point -2,3,-1   and vector 3i-2j

Q: Sketch the following vectors u, v and u*v as vectors starting at the origin u = -2i + 2j and v = i -…

A: In coordinate system, xi +yj +zk can be written as -  (x,y,z)

Q: Find a unit vector u in the direction of v. Verify the ||u||=1. v= (-8,-2) u=

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Q: Find the angle θ between the two vectors.u = (0, 4, 0, −1), v = (1, 1, 3, −3)

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Q: A. Give the Cross products of the unit vectors (i, j, k).

A: Understanding of cross product of three vectors are required to under this.

Q: Consider the vectors u = ⟨cos , sin , 0⟩ and v = ⟨cos , sin , 0⟩, where &gt; . Find the dot product…

A: Consider the given vector u→=cosA,sinA,0 and v→=cosB,sinB,0

Q: Find a unit vector perpendicular to the plane of P(1, -1, 0), Q(2, 1, -1), and R(-1, 1, 2) .

A: Given P(1, -1, 0), Q(2, 1, -1), and R(-1, 1, 2) .

Q: Find the vector v with the given length and the same direction as u.||v|| = 3, u = (0, 2, 1, −1)

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Q: Define the vectors u = и %3 (-5, 2, –1) v = (3, 2, –5) - а)Compute u: 0. b)Is the angle between u…

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Q: ind the cross products u×v and v×u for the vectors u=2,4,0 and v=0,3,−

A: To find the cross products u×v and v×u for the vectors u= (2,4,0) and v=(0,3,−6).

Q: Find the cross products u×v and v×u for the vectors u=2,3,−7 and v=1,−1,1.

A: vector or cross product

Q: Find the angle a between the vectors 5 2 and 1 a =

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Q: Use the vectors u = (1,-3,5) and v=(2,1,-3) to Find a. cos(theta), where theta is the angle between…

A: As we know that; The expression for the dot product between the two vectors u &amp; v is: u·v=uvcosθ…

Q: Find a unit vector u in the direction of v. Verify that |u| = 1. %3D v = (1, -7) U =

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Q: Use vectors =(-1, 1), v= (7, –2), and w= (0, 4) to find (u w)v, and determine whether the result is…

A: We can answer it as below

Q: Find a unit vector that is orthogonal to both u and v. u = (-8, -6, 4) (17, –18, –1) V

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Q: If u is a unit vector find the dot product of vectors u and w

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Q: Find the angle between the vectors v and w v = (−2, 3, 1)T , w = (1, 2, 4)T

A: Consider the given vectors: Here the objective is to find the angle between vector v and w.

Q: Find the angle θ between the vectors.u = (0, 1, 0, 1), v = (3, 3, 3, 3)

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Q: Compute the dot product of the vectors u and v, and find the angle between the vectors. u= (-11,0,5)…

A: To find the dot product and angle between the two vectors u and v.

Q: compute the dot products i ⋅ j, i ⋅ k, and j ⋅ k for the unit coordinate vectors. What do you…

A: Given: Compute the dot products i ⋅ j, i ⋅ k, and j ⋅ k for the unit coordinate vectors.

Q: Find the angle θ between the vectors.u = (2, 3, 1), v = (−3, 2, 0)

A: Given: u=2,3,1, v=-3,2,0 we know that angle θ between two given vectors A=x1i+y1j+z1k, B=x2i+y2j+z2k…

Q: Find the unit vector u in the direction of v. Verify that u| =1. 12. (1,–6)

A: solution is given below..

Q: Find the angle e between the vectors. u = (0, 0, 1, 0), v = (3, 3, 3, 3) radians

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Q: Find the angel between the vectors u and v if u=-4i+2j and v=3i+2j Round answer to two decimal…

A: Consider the dot product of two vectors.

Q: Use a dot product to determine whether the vectors u = ⟨1, 2, 3⟩ and v = ⟨4, 1, -2⟩ are orthogonal.

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Q: Find a unit vector u in the direction of v = 〈6, -1〉. Verify that ⎥⎥ U⎥⎥ = 1

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Q: Find a unit vector that is perpendicular to both u = (1,0, 3) and v = (-1,2,0). Answer:

A: We have to find the unit vector which is perpendicular to given vectors.

Q: Find a unit vector u in the direction opposite of v = (2,8,-3).

A: Solution ) v =  { 2 , 8 , -3 }   vector with same magnitude and opposite direction   = { -2 , -8 , 3…

Q: perpendicular to the plane formed by the vectors w1 = [1 2 1] and w2 = [2 2 3], with the z axis

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Q: Find the angle a between the vectors 3 a || -1 -2 - and 1

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