1. Perform the stated operations on the vectors u, v and w. (e) -8(v+w)+2u (f) 3w-(v-w)

Q: B) Given the vectors u = 7i+ 2j -k, v = 2i-3j-6k. Find the projection of %3D u onto v.

A: Using projection vector formula.

Q: If v . w = 0, then the vectors v and w are________.

A: Lets two vector be v and w. v.w = v × w × cosθ Where theta is angle between v and w.

Q: a vectors p = (2) and t = (,).

A:

Q: 4 9. is 6/2 The distance between the vectors u = and y = -2 %3D -5 True O False

A: Suppose u and v be any vectors from a same vector space. Then the distance between u and v is…

Q: let v = (1, 3, −2) and w = (2, −1, 4). Find all the vectors orthogonal to both v and w.

A: Given: The vectors v=1,3,-2 and w=2,-1,4. To find: The vectors orthogonal to both v and w.

Q: 2 7 Consider the vectors: u = 1 v = -1 w = -2 2 Express W as a linear combination au + bv. What is…

A: follow next step

Q: Which of the following vectors is orthogonal to the plane 3(x - 7) + (y + 8) - 5z = 15? O O O

A: Given equations of plane 3(x-7) +(y+8)-5z=15this is an equation of the form a(x-x1)+b(y-y1)+…

Q: \(\) The vectors u= and V = are not orthogonal if and only if x=-136

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Q: If v=3w then the two vectors v and w are ................

A: Given :                    If v = 3w, then the two vectors  v and w are ____________

Q: 4. Find the vector equations for the line of intersection of the following planes: 2x – y – 5z = -14…

A:

Q: In Problem,decompose v into two vectors v1 and v2 where v1 is parallel to w and v2 is orthogonal to…

A: V=v1+v2  (Given)when two vector v1 & w are parellelthen the angle between v1 &w is 0° or…

Q: Suppose vectors v, w, and z sum to the zero vector. If v = 8.2i - 3.8j and w = 4.1i + 1.3j, find z.

A: We have to solve

Q: 10. Given two vectors u = [2,4] and v = [6,2]. determine the projection of u on v.

A:

Q: Consider the points P(3, x, -2) and Q(5, 3, 4) in R3 . Find x so that the vector from P to Q is…

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Q: If y is orthogonal to the vectors u and v, then y is orthogonal to u+ 3v. True False

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Q: Find the value of t such that the vectors v=(2t+1,-3,3t-2) and w=(7,4t+2,2) are orthogonal.

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Q: 4. Using the vectors: ü=[2,-1,3], v=[4,5,-2], w=[1,-1,7], calculate: a) b) ux v c) ū+ v +2w

A: Here we have to perform the vector operation

Q: If v.w 0, then the vectors v and w are

A: We know that two vectors u and v are said to be orthogonal if u . v = 0.

Q: 4 r 1 by -1 -2 -3 -4 -5 -4 -3 -2 -10 1 2 3 4 5

A: First we find p, q, r and s. Then solve it.

Q: 2. If å and b are two vectors with lengths 2 and 5 and angles between 150°, respectively, obtain the…

A:

Q: Consider the vectors: u=(-2,6), v=(-3, –4), w =i+9j, and x=8i-6j.

A:

Q: For what value of c is the vector v = ⟨2, -5, c⟩ orthogonal to w = ⟨3, 2, 9⟩?

A: Two vectors are said to be orthogonal if their dot product is zero.

Q: Suppose u and v are two vectors. Then (2u + v) · (u x v) = 0, always. O True O False

A: (u x v) is the cross product of u and v. And it is perpendicular to both u and v.

Q: Which vector below is NOT orthogonal to i = -2î – 8ŷ + 7k ? -- 1 2 8. O 0 î + 0ĵ + 0k 3. 1 O 4 î - )…

A: Given problem:-

Q: 2b.) Suppose u, w are two vectors in R' satısfyıng uXu = 4, wXw uxw = 8. What is the distance…

A: Given u and v be two vectors in ℝ7 satisfying u×u=4, w×w=16, u×w=8

Q: Find the angle between the vectors r = (-1, 2) and s = (4, 2)

A:

Q: What can be said about non-zero vectors ū, v and w if (ūxv)· w = 0?

A: Here use the definition of cross product and dot product of vector

Q: 5 Given that p andr , find in column vector form: 4 p-r ep-2

A:

Q: If u, v are vectors such that |u || - 3, ||v|| - V5, and u v- 1, what is |u + v|| ?

A:

Q: 10. Which of the vectors U =, V = and W = are in the same plane?

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Q: what is u.v when u and v are two unit vectors with an angle of (pi/6) between them. if u=i and if v…

A: Given: u=i, angleθ between u and v=π6 let's assume v=xi+yjx2+y2 we know that angle between two given…

Q: 1. Given three vectors u =(1,–3,0), v=(2,1,–1) and w=(0,2,3). Determine: a. Bu + 4v – Sw]. b. Cosine…

A: 1. a.

Q: Find the vector v with the given length and the same direction as u.||v|| = 5, u = (√5, 5, 0)

A: Let the vector u is:   Now, The modulus of vector u is :                                     The…

Q: (a) Suppose that a and b are two unit vectors in R^3, and a·b=11/24. Find the norm of the vector 4a+…

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Q: 8. If the vectors in the figure satisfy |u| = |v|= 1 and u + v + w = 0, what is w ? u W V

A:

Q: 2a.) Suppose u, w are two vectors in R7 satisfying uxu 4, wxw 16, uXw = 8, What is the cosine of the…

A: We are given that : u→.u→=4⇒u→u→cos 0=4⇒u→2=4⇒u→=2 w→.w→=16⇒w→w→cos 0=16⇒w→2=16⇒w→=4 Now, Let θ be…

Q: 2. (a) Compute ||(1,2, 3)||- (b) Find the angle between the vectors (1, v3) and (1,0).

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Q: -6 --5 Let z = and y . Find the vectors v = 47, ủ =i + ÿ, and w = 47 + y. w = || ||

A:

Q: b. Find the angle between the vectors u = (18, –1, –7) and v = (-37,35, 2)

A: u = (18, -1, -7),  ∥ u ∥ = √[(18)2+(-1)2+(-7)2] = √374 v = (-37, 35, 2), ∥ v ∥ =…

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: 20. Show that the pair of vectors ' and ¯J is perpendicular.

A:

Q: The distance between vectors v1 = (2, 1, -4) and v2 = (1, -1, -2) equals: Select one: O a. -2 O b. 3…

A: To find The distance between the two vectors v1=(2,1,-4) and v2=(1,-1,-2)

Q: Find the vector z, given that u = (6, -3, 2), v = (0, 2, 1), and w = (-6, -6, 2). %3D Z = -u + 4v +…

A:

Q: Find the vectors that satisfy the stated conditions. 23. (a) Oppositely directed to v (3,-4) and…

A: a) The given vector is v = <3, - 4>  To find vector opposite to given vector and half in…

Q: O Are the three vectors: V= 4i-8j+kV= 2i+j-2k and ū;=3i-4j+12K in the Same Plane?

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Q: Find the vector v with the given length and the same direction as u. ||v|| = 3, u = (1, 0, 1, –4)

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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: et x = [7, -4, -8] and y = [-6, -6, –10] be vectors in R'. Compute the following: %3D a+y [ -8x = […

A: Let's find.