(a) Consider two vectors u = 3 and v = 5 in R4, Show that 5 7 7 i) u.v = v.u ii) d(u, v) > 0 [-31

Q: The vectors u-(2,-1,1) and v= (1,1,2) in R3, the angle e between u and v is

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Q: u and i are vectors of R" such that ||ū|| = 3, |||| = 4 and the angle between them is. Determine the…

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Q: C A

A: We use Triangle law

Q: (b) Find the angle between the vectors u and v if u = (2,3,5) and v = (1, -4,3) in %3D R3.

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Q: Find F‘(0)  for the function f(x)=3xe5x b) Given vectors a=(1,3,-2) and b=(1,1,2) , find  3a +2b…

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Q: What is the unit vector oppositely directed to 4?−5?−5??

A: Topic:-  vector algebra

Q: Suppose V₁, V2, V3 is an orthogonal set of vectors in R5. Let w be a vector in Span(V1, V2, V3) such…

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Q: Consider the vectors u=(2,3,-5), V = (-3, -2,6) and w=(-4,8,4). Calculate u.v

A: We have to find u.v

Q: 2. Consider the two vectors in R³ with components u = (2,-1,-1) and v = (-2,1+ √√3,1-√3). (a) (12…

A: Step 1: Step 2: Step 3: Step 4:

Q: Consider vectors u and v. Find the following. (a) u v (b) u.u u = (-3, 0, 3), v = (-1, 6, 1) (c)…

A: The given vectors are

Q: find the diJ tance betueen the vectors

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Q: 21A)The vectors A = 3i+j+ 4k, B = 2i - 3j-k, and C = i-2j+ k, find (A x B).C

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Q: The vectors u = (-7, 1, -2) and v = (-28, x, - 8) are parallel if and only if x = - 212 %3D Select…

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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: 7. Consider the following two vectors: u = (5, –3) and v = (2,3) (a) Evaluate |u| and |v|. (b) Find…

A: As per guidelines, we are supposed to do only the first three parts of multipart question. If you…

Q: Let the following vectors be in R³ a = (1,3,-1) b= (-2,1,3) c = (3,2,1) d = (1,-1,2) 15.- Find the…

A: Introduction: Vector Operations are operations that are performed on vector quantities. Vector…

Q: Find the values of x such that the angle between the vectors and is 45°.

A: Given that The angle between the vectors 6,1,-1 and 1,x,0 is 45°.

Q: Find the angle between the two vectors u 2i+ j-7k and v =i-j+ 4k

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Q: : (2,1,2). 1- Find the unit vectors u1 and u2 in the directions of v = (1,3) and w = Find unit…

A: If we have a vector u=a,b,c, then the unit vector that is in the direction of vector u is the vector…

Q: Let a and b be two unit vectors. 1) a x (a.b) 2) a . (axb) 3) a . (a+(axb)) 4) (axb) + (bxa)…

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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: Determine by inspection the linearly independent vectors !! O a. O b. O C. с. -8 12 4 -2 2 5112]…

A: To determine by inspection the linearly independent vectors.a -812-4, 2-3-1, 000b 51, 28c 4-26, 6-39…

Q: 7. Find all values of x that make (x, 1, –3) and (x, 2, x) perpendicular vectors.

A: I am attaching image so that you understand each and every step.

Q: What does (a b c)=0 imply with respect to the vectors: a,b,c

A: Consider the given information. The given vectors are a, b and c. Geometrically, the scalar triple…

Q: If u • vx w or v • or w • v equal to zero, then the vectors u, v , and w are coplanar... True False

A: Concept Used: Three vectors are said to coplanar if their scalar triple product is zero That is  [u→…

Q: Let W be the set of all vectors of the form 111 ū= -3s- 2t 2s+t -s-2t Find vectors u and 7 in R³…

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Q: Find the angle between the vectors v and w v = (−2, 3, 1)T , w = (1, 2, 4)T

A: Consider the given vectors: Here the objective is to find the angle between vector v and w.

Q: For the vectors u = (- 1,3) and v= (-4,2), calculate proj,u and scal,u. proj, u = D

A: Vector and scalar projection