Problem #8: Let R have the Euclidean inner product. Find a unit vector with a positive first component that is orthogonal to all three of the following vectors. u = (1,-1, 7, 0), v= (8, 1, 0, 1), w= (1, 0, 3, 1) Enter your answer symbolically, as in these examples Problem #8: Enter the four components of your vector, separated with commas.

Q: 1. Let u, v, w be the vectors in the following picture. Which of the following vector equations is…

A:

Q: 7. Assume vectors V₁, V2, V3 are nonzero. Explain why the set S = {V1, V2, V3} is linearly dependent…

A: This question examines the linear dependence of three non-zero vectors v1,v2, and v3, where v3 is…

Q: Consider the vectors v = [1, 2, 4, 6] and w = [2, -1, 2, -2]: (a) Decide whether the vectors are…

A:

Q: Given vector v = (-6, 4), find -0.5v graphically by stretching the vector by its tip and then…

A:

Q: 3. Determine which of the pairs of vectors are orthogonal. (a) a = (b) u = (c) y = 8 12 -5 3,0 = -3…

A:

Q: Let Are the vectors 7₁, 72 and 3 linearly dependent or linearly independent? linearly dependent [8]…

A:

Q: If V is a vector in R³, then what can we say about the expression V.V.V?

A: Given that V is a vector.

Q: This question comes from the material you covered independently in chapter 3. Consider the vectors u…

A: Vector addition or vector subtraction of two component vectors can be determined by adding or…

Q: ach of the following sets of vectors in R³, say whether the vectors span R³. Support your ers with…

A:

Q: Express the vector in the form v = vji + v2j + v3k. AB if A is the point (-9, -5, 5) and B is the…

A: A-9,-5,5 and B-4,-12,8

Q: If u = and v = , find 1/3u - 2v.  (this is a vector problem)

A: Given,  u = < 3 , 9 > and v = < -3, 1 >,

Q: Let S be a finite set of distinct nonzero vectors in R¹2, and |S|=the number of vectors in the set…

A: given that⇒S be finite set ofdistinct non zero vectors in ℝ12 and |s|=14

Q: 2. Find all vectors [10] [8]. so that the following vector equation can be solved for c₁ and c₂: [T]…

A: