For each statement, determine whether it true or false, and justify your answer. a) In R³ if two lines are not parallel, they must intersect at a point. b) For u, v, w in R", if u +w=+w then u = v. c) There are no vectors u and 7 in R" such that ||ū|| = 1, ||v|| = 3, and ū - v = 6.

Q: If ū and i are two vectors, prove the identity ld + 레? + |d - 비? = 2| + 2|미2

A: This question is based on vector multiplication.

Q: ude 5. Find the area of the triangle created by the

A: Given a, b and c are three vectors with the same magnitude 5.

Q: What geometric relationship must two vectors have in order for ||u + v|| = ||u|| + ||v|| ?

A: The expression ∥u+v∥denotes the norm of u+v, ∥u∥denotes the norm of u and ∥v∥denotes the norm of v.…

Q: u = (5,-1, 2) and v = (2,-1,-3) Compute the following: a.) v b.) lul c.) uv d.) projuv e.) The angle…

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Q: Let a. h and care vectors such that a = 3. b = 4 and | C| = 5, and (a+b) is perpendicular to -- c.(b…

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Q: We have vectors U and V such that u|| v. If u-(5,6,7) and v=(a,-18,c), with a and c real constants,…

A: We have to find a.c

Q: Let ū= (2,3,-5) and = (-4,-6,5). Determine a vector equivalent to 2 - 3 v Express - using unit…

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Q: Suppose that u,v are two vectors such that Ju| = 3 and |v| = 4. Let 0 represent the angle between u…

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Q: I) Which of the following expressions represent vectors? (Zero or more options can be correct) r a)…

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Q: Vectors in R must have two or more values. A) True B) False

A: Ans: B) False

Q: 39. The vertices A, B, C of a triangle have position vectors a, b, c respectively. The area of this…

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Q: -> Let a, b and care vectors such that a = 3, | b = 4 and = 5, and (a+b) is perpendicular to c.(b +…

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Q: Suppose that u and v are vectors in R7 both of length 2√2 and that the length of u - v is also²√².…

A: Solution :

Q: → ->> Let a, b and care vectors such that a = 3₁ | b = 4 and 5, and (a+b) is perpendicular to = → ->…

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Q: If 7, r, and r, are three parallel vectors of the same magnitude Prove that i+r, +r, is equally…

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Q: 4. a) Givenā = [-5, 2, -3],6 = [7,-4, 1], c = [x, -2, z], and a × c =b, find x and z. b) Find a…

A: Given,  a→=-5,2,-3,  b→=7,-4,1 , c→=x,-2,z

Q: The vectors į+j and i-į are perpendicular. True False

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Q: Prob. 2. ū and i are two vectors. If |피 = 4, [히 =3 and 2(ü, ü) = 2π/3. Find: a) ü.ㅎ b) ū.u c) |3ü +…

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Q: -El--E--E| a) Consider a set of vectors, x =|3 ,y =| 2 , and %3D 14 Can we express the vector, v = 4…

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Q: Lets vectors V and U be such that |v|=3 and |u|= 4. the angle between v and u is 30 degrees. find…

A: Given: u→=4    and   v→=3 Angle between vectors u and v is: 30°

Q: 28. Prove that if A and B are any nonzero vectors and C- BIA + JAB, then the angle between A and C…

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Q: 1) Which of the following expressions represent vectors? (Zero or more options can be correct) r a)…

A: Step:-1 Vector:- A vector is a quantity that has both magnitude and direction and vector is…

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: 2) Given the vectors a-[4, 2, -6], b-[6, -3, 2], and c-[-5, 0, 4], simplify the following vector…

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Q: State the condition(s) that: a) two vectors can be equal vectors. b) two vectors can be opposite…

A: To state the conditions for a given vectors.

Q: 21. Given vectors u = (1,3) and v = (-6,2). a) Find u - 3v b) Find Ju + v].

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Q: 1 b. O Find a, b and c given that 2 За 2 a [ii] Vectors 3 -6 are parallel. Find a and b. and -4 b. 3…

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Q: Quolel X= -gi +sj -K, Y. i-2 k yo i-2 K Find X x Y

A: (1) Consider the given vectors x=-2i+3j-k and y=i-2k   We have to find x×y   Now, x×y=ijk-2   3-11 0…

Q: For the following, let u = (3, –6) and v = (2, 1) %3D a. Find u + 3v b. Find the angle between the…

A: Hey, since there are multiple sub-parts posted, we will answer first three sub-parts. If you want…