Suppose a and b are nonzero vectors in R2, c is the orthogonal projection of a onto the line spanned by b (that π is: c = proja), and the angle between a and b is 3 Which of the following is NOT true about the relationship between a, b and c? Select one alternative: ○ (a — c) · b = 0. a is a member of span{b}. ||c|| |||a|| ` C = kb, for some real number k. O cos (F) 3 =

Q: 1. Given the points P(5, 3, - 4) and Q(7 - 1, - 3), find the following: a. the vector PO b. PQl

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Q: -21 6. Find h so that the vectors 1 is in the span of the vectors 4, and -3 -0-

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Q: Use vectors to find the lengths of the diagonals of the parallelogram that has i+j and i – 2j as…

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Q: Suppose that u and v are two vectors with |u| = 1, |v| = 4 and u · v = −2. a. Compute |u + v|. b.…

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Q: Let* be the angle between the vectors ₁ and ₂. Let be the angle between the lines l₁ and ₂. We have…

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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: 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: 7. Let -4 4 a. How many vectors are in {V1, V2, V3}? b. How many vectors are in Col A? c. Is p in…

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Q: If some p vectors can span V, then dim V= p True False

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Q: -15). Let y = a and the vector 2 = ba CM and let L- Span pan{[+]} [2] is Write y = y + z. where the…

A: Given that y=-51 and let L=span-11. We have to write the vector in the form y=y^+z, where y^=ab is…

Q: Suppose that u, v, and w are vectors such that = 3, = -2, = 5, llull Evaluate the following…

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Q: Show that if the vectors v, w are orthogonal, then ||v + w||^2 = ||v||^2 + ||w||^2.

A: Given: The vectors v, w are orthogonal, then ||v + w||^2 = ||v||^2 + ||w||^2.

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: Suppose à and are arbitrary vectors in R³ such that ||a|| = 1; |||| = 4; Let c = (2a × b) — 36. Find…

A: For given conditions we have to find the angle between  vector b and vector c.

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. Find the area of the parallelogram spanned by the vectors a = (1,0,1), b=(-2,1,2) A. √5 B. 3 C.…

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Q: Use a software program or a graphing utility with matrix capabilities to write v as a linear…

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Q: 7. Write the vector w in terms of u and v, given that the terminal point of w bisects the line…

A: This question is related to vectors, we will solve it using given information.

Q: M3. Which of the following expresses the fact that the vectors u and v have the same length? (a) ū -…

A: M3. The two vectors u and v have the same length if: (a)u→·v→=v→·u→

Q: 12. Given a point P(1,-2,-4) and a point P2(3,1,-5), find a unit vector that has the opposite…

A: Step 1:Step 2: Step 3: Step 4:  thanks...

Q: Let vi = 2 v2 , V3 = -3 3 Does the set of vectors {v, ,v2, v3} span R3 ? Give reason(s) for your…

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Q: 2. Let x and y be vectors in R³. Prove that y=(|x +ỷ1² − |x|² − |ÿ1²): a) Using a geometric…

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Q: This exercise illustrates how vector arithmetic can be used to prove propositions in plane geometry.…

A: (a) Here, u=v=u+v=1. ⇒u2=v2=u+v2=u+v·u+v ⇒(u+v)·u+v=1⇒u·u+2u·v+v·v=1⇒u2+2uvcos(θ)+v2=1⇒1+2…

Q: 2a.) Suppose u, w are two vectors in R7 satisfying uxu 4, wxw 16, uXw = 8, What is the cosine of the…

A: We are given that : u→.u→=4⇒u→u→cos 0=4⇒u→2=4⇒u→=2 w→.w→=16⇒w→w→cos 0=16⇒w→2=16⇒w→=4 Now, Let θ be…