38. Let u and y be nonzero vectors in 2- or 3-space, and let k = ||u|| and I = |v. Prove that the vector w = lu + kv bisects the angle between u and v.

Q: Consider three vectors u = 3i +j+ ak, = 2i + bj +k, = -4i + (b – 2)3 + (b+ 8)k, where a and b are…

A: The solution are next step

Q: Show that the vectors i - j, j - k, k - i are parallel to a plane.

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Q: 18) a) Find a unit vector that is orthogonal to both u = and v = . b) find the area of the…

A:

Q: Find a vector v such that v = 15 and v is in the same direction as –li + 13j

A: The solution is given as

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

A: Two vectors are orthogonal, if their dot product is equal to zero.  The formula to calculate dot…

Q: 1. Using the vectors u = [4, -3] 3 = [7, 1] and w = [-5, 3], evaluate the following, if possible. If…

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Q: 1) a) Find all vectors such that X = b) Explain why there is no such that X =

A: It is required to find all the vectors v→ such that 1,2,1×v→=3,1,-5. It is required to explain why…

Q: n Let ú and ú be two nonzero vectors in R" for which ú + 2v is orthogonal to ủ – 20. What is the…

A: We have to find the ratio

Q: Use the cross product to determine the angle between the vectors [4, 5, 2] and= [-2, 6, 1]. Verify 9…

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Q: Find the unit vectoru in the di rection of the vector v= 2( 5, 0, 12 ). 1 u = V A. 52 1 u = 26 В. 1…

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Q: "ove that if two vectors are linearl y de pendent, e of them is a scal ar mul it ple of the other.

A: Two vectors are linearly dependent, one of them is a scalar mulitple of the other.

Q: 4. Consider the vectors u,v and w are defined, u = 3i-j+4k, v = 4i – 2j +6k and w= 5i+2k (a) Express…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: For the vectors u= ,0,2) and v= ,- 3), calculate projyu and scal, u. projy u = O DD

A: Given ,the vectors u=-4,0,2  and   v=1,3,-3

Q: 10) Find two vectors of norm 1 that are orthogonal to the vectors u = and

A: Consider the provided question, u=12-23 and v=2134 Let w=ABCD be such a vector,Then, w·u=0…

Q: -> -->> u, v and w are three non-coplanar unit vectors and a, ß and y are the angles between u and…

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Q: u * v =( u1v1, UzV2 , Uz V3 , · Un Vn).

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Q: Let u=j-5k, v=5i-j+k, w=-10i+2j-2k Which vectors, if any, are perpendicular? Which are parallel

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Q: Let u= : (−5, 1, 4) and v = (3, 0, -6). Use the cross product to find a vector that is orthogonal to…

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Q: Let a,b be scalars. Find a vector perpendicular u=

A: Given u = <a,b>                   a,b are scalarlet v be the vector perpendicular to uv =…

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 length of the vector v = (9, 3, 9). ||v|

A:

Q: 3. Determine whether the vectors u and v are orthogonal, parallel or neither. (show/explain your…

A: (a). Given ,  u = 2,3,-1 and v = -1,-1,-1 (b). Given , u = j + 6k and v = i - 2j -k

Q: Find the vector projy u. v = k, u = 6i + 9j + 2k A. k 121 В. 2k 18 i+ k С. O D. 121 i+ 121 + 121 k

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Q: 79. Show that if a, b are nonzero vectors such that a 1 b, then there exists a vector X such that a…

A: To show a×X=b if a, b are nonzero vectors and perpendicular to each other.

Q: Let z, w e C. Clearly prove that z+w = z + w.

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