In Problems 40–45, use the vectors v = 3i + j - 2k and w = - 3i + 2j - k to find each expression. 40. 4v - 3w 41. || v - w || 42. || v || - || w || 43. v * w 44. v . (v * w) 45. Find a unit vector orthogonal to both v and w.

Q: /. Find the general solution of the following Initial Value Problem (IVP): y +9y-10y = -40t²-72t + 8…

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

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Q: Find all the vectors x* that minimize||Ax – b||, where A and b are as given. [2 1] A = 2 4, l3 3] -3…

A: To find - Find all the vectors  x* that minimize Ax - b, where A and b are as given. A = 212433, b =…

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A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

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: 16 Jlg wo vectors ñ and m are said to be orthogonal if ħxñ=0 ulgo O ihs o

A: Two non-zero vectors are said to be orthogonal when (if and only if) their dot product is zero.

Q: +5 c) Let y = n44| and u = is Span{u} and one orthogonal to u. where n=9. "t. Write y as sum of two…

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Q: EX/ Find The normal vector to A = 2i-3j+4K, B =i-2j+ 5K %3D ĀxB =Ñ =1? ĀXB=N -3 4 = -7i-6j-K %3D - 2…

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Q: (a) What is the sum V of the twelve vectors that go from the center of a clock to the hours 1: 00,…

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Q: 1. Compute the following for the vectors in R3, x [1 3 21T and y [40 1T y and y x (a) (b) 2 and y2…

A: From the given information, [1 3 –2]T and [4 0 –1]T.

Q: Let r, y, z be (non-zero) vectors and suppose w = 4y – 16x + 3z. If z = 4x – y, then w Y. Using the…

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Q: 2. Find the magnitude of the vector PQ whose initial point is P(1, 2) and end point is at Q(4, 3).

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

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Q: Problem 12. True or false: If we know T(v) for n different nonzero vectors in R", then we know T(v)…

A: we have to see if  we know the value of T(v) at n different non zero then can we know T(v )

Q: Find the general solution to the following vector DE. 1 æ[t) = | -2 1

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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: Suppose that u, ū, and w are vectors in R3 such that ūxi = (2,7, 3) and ūxu = (-5, 4,0). Find: 1.…

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Q: 3. The work Wdone by = xf + 3xyj - (x + z)k to move a particle from point 1 to point 2 is defined by…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

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A: According to question, Given system, X '⇀t = 1243 X ⇀t

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A: Given components of two vectors: Components of a are: ax=2.0 units and ay=3.0 units, Components of b…

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

A: WRITE  W AS A LINEAR COMBINATION OF U AND V ie. w = au + bv Using Row Elementary Transformation,

Q: If u = x2 + 2x -y and v = - 2xy- 2y, then the vorticity vector is - 3yk 10 -yk 110 YK III

A: We have to solve given problem: Concept:

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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: 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

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Q: decompose v into two vectors v1 and v2 , where v1 is parallel to w, and v2 is orthogonal to w. 25.…

A: This question is related to vector. We will solve this question by using property of vector.

Q: For what value of k, the vectors (-1,0,1), (2,1,A) and (3k+2, 3,10) are lincarly dependent. O A. 1…

A: We have to find for what value of k, the vector -1,0,1, 2,1,4, and 3k+2,3,10 are linearly dependent.

Q: 11. What is the vector which is orthogonal both to 9i + 9j and 9i + 9k? B. 81i – 81j – 81k A. 81i +…

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Q: Q1) If a vector gets multiplied by a positive number, its direction * .will be reversed

A: Given statement : If the vector gets multiplied by a positive number, it's direction will be…

Q: QUESTION 9 Let u and a be two vectors in Rn with a o Then, āx (ū-Projzū) O None of these options is…

A: Let's find

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A: To solve question 3 I will take the help of eigenvalue and eigenvector of a matrix because question…

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

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Q: Q3/ Show that the vectors (2i + 3j + 6k), (3i – 6j + 2k)and (6i + 2j + 3k) Are mutually…

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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: The opposite vector of 10 N [S80°W] is 10 N [W10°S]. True False

A: Please see the below picture for detailed solution.

Q: TRUE/FALSE If x and y are nonzero vectors in Rn and A = xyT , then the row echelon form of A will…

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Q: 2. For what values of h the vectors , ü2 = 9 ,ūz linearly independent? are

A: To find : For what value of h  given vectors are linearly independent    We have given the…

Q: 13. Describe the vector that translates LMN to L'M'N’. 6. L' L 2 N' M -6 -4 -2 4 6 N2 M -4 -6 4,

A: Translation vector

Q: 17 jp 17 Jlgull>> حفظ الإجابت 3 درجات Two vectors ñ and m are said to be parallel if ñ m-0

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Q: 1. If vectors u (3, 3), v-(13.-7), and 2w +3u-v 2. When is it true that u+ v=v+u?

A: The symmetric property states that for all real numbers x and y, if x=y, then y = x SO,  u+v =v + u

Q: Find the values of x, y and z that satisfy the vector equation 1 3 ·¤-A-D-A-A-D 3 +y-2 +2 1 1-2 +3…

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Q: 10. Suppose A, B, and C are vector functions whereas 1, w, and are scalar functions, which of these…

A: Determine each of the given options for their correctness. Option (A): On the left hand side: ∇∇…

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A: Given: A vector a∈ℝn and a scalar λ>0   To show: The problem minx12x-a22+λx2 has the optimal…

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Q: 3. Describe the vector that translates DEF to D'E'F'. O (3,4) O (-3,-4) (4,3) O (-4,-3) ô -5 -4 -3…

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