Finding Orthogonal Vectors In Exercises 65–68,find two vectors in opposite directions that are orthogonalto the vector u. (There are many correct answers.)65. u = ⟨3, 5⟩ 66. u = ⟨−8, 3⟩67. u = 12i − 23 j 68. u = −52i − 3j`

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Q: Finding the Direction Angle of a VectorIn Exercises 61–64, find the magnitude anddirection angle of…

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Q: 23. Are the vectors u = and v = orthogonal? Explain.

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Q: Orthogonal means being [ Select ) To determine if two vectors are orthogonal, check if their (Select…

A: follow the procedure given below.

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Q: Length and DirectionIn Exercises 25–30, express each vector as a product of its length anddirection.

A: Given: 1)(2i+j-2k)

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Q: What is the unit vector for the vector (-9.53, 13.04, –13.15)? Answer: ( Nete

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Q: 7. Find the real part of the dot product of the vectors u" = (i, 1+ i, 1) v* = (5 + i, –2 + 2i, –1+…

A: Dot product of complex numbers

Q: Vector Operations In Exercises 29–32, find (a) u – v, (b) 2(u + 3v), and (c) 2v – u. 29. u = (4, 0,…

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Q: 5. Find the real part of the dot product of the vectors u" = (1 – i,1+ i) v° = (5+ i, –3 – i)

A: SOLUTION:

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Q: linear combination of the standard unit vectors i and j.

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Q: Determine if the vectors are linearly independent Justify your answer. 6. 12 - 36 The vector…

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Q: QUICK CHECK 6 Verify that the vector (is. 15) has length 1. <

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Q: Working with vectors Let u = ⟨2, 4, -5⟩ , v = ⟨-6, 10, 2⟩ , and w = ⟨4, -8, 8⟩ . Compute u - 3v.

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Q: 4. Determine if the vectors are orthogonal, in the same direction, or neither. Briefly explain your…

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Q: Test I: Determine whether u and v are orthogonal vectors. 1. u = (6,1, 4), v = (2, 0, -3) 2. и %3D…

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Q: Check whether the sets of vectors (i) ā = {1, 1, 1}, b = {1, 2, 0} , ĉ = {0, – 1, 2} and (ii) ā =…

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Q: Use a software program or a graphing utility with vector capabilities to find the lengths of u and…

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