In a 4-D Euclidean plane, vectoru = (a, b, c, d). In a 3-D space, vector v = (2,7,c). What is u + v? A. ((2+a), (7 + b), 2c) B. ((2+ a), (7 + b),c, (c + d)) C. ((2+ a), (7 + b),2c, d) D. ((2+ a), (7 +b), 2c,0)

Q: Consider the vectors [2, 1,0, 2|], [3, 1,0, 1), [1,1, 0, -1] in R. Decide whether they independent.…

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Q: What is the size of the space stretched by the vectors {(1,0,2),(2,1,4),(1,-1,1)}?

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Q: Find a unit vector perpen dicular to the plane of the vectors a = (2, -3,1) and b = (1, 2, -4)

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Q: Find the shortest distance from point P = (1,2,-3) to the plane which passes through (2,3,-1) and…

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Q: A vector orthogonal to the plane through the points (-1,0, 0), (0, 0,-2), (2, 3, 4) is

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Q: . Find two vectors that are orthogonal to the plane containing the points P = (3,0,1), Q = (4, -2,1)…

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Q: Consider the vectors (2, 1, 0, 2], [3, 1,0, 1], [1, 1, 0,-1] in R'. Decide whether they independent.…

A: Given: Vectors in ℝ4,                              2,1,0,2, 3,1,0,1, 1,1,0,-1 To find: Whether the…

Q: Show that the vectors ⟨1, 2, 3⟩, ⟨1, 1, 0⟩, and ⟨3, 4, 3⟩ lie in the same plane

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Q: The unit vector in 2-space that makes an angle of π/3 with the positive x-axis is _____

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Q: The sum of the squares of the direction cosines of a vector in space add up to ..............

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Q: Are the vector spaces R4, M2,2, and M1,4 exactly the same? Describe their similarities and…

A: We have to determine if the vector spaces, are exactly the same or there is any similarity or…

Q: 2- Are the vectores [4,2,6] and [6, 3, 9] collinear? How do you know?

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Q: Determine whether the vectors a = (1,2,3),b = (1,3,1),c =(2,2,2) plane? coplanar, that is, they lie…

A: Answer and explanation is given below...

Q: A vector orthogonal to the plane through the points (-1,0,0), (0, –2, –2), (2, 3, 4) is

A: Query- Find a vector orthogonal to the plane through the points -1,0,0,0,-2,-2,2,3,4. Answer- Let…

Q: What is the area of the parallelogram determined by the vectors v = (1, 3, 6) and w = (-1,0, 3)?

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Q: are the vectors u=(-4,2) and v=(-1,2) orthogonal, parallel, or neither?

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Q: Give a vector of length 13 that is parallel to (-1,2, –2).

A: Topic- vector calculus

Q: What is the length of the vector (1, 4, 5, -3) in R^4?

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Q: Give an example of a non zero vector that is perpendicular to (5,7,4)

A: We know that "two vectors are perpendicular to each other if and only if their dot product is zero"…

Q: The plane that contains the points (-2,1,0), (1, 0, –1) and (0, –1, 1) is orthogonal to which…

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

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Q: Express A = (3, 1, – 1) as B+ C, where B is parallel to the vector (1,4, 2) and C is perpendicular…

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Q: A vector orthogonal to the plane through the points (-1,0,0), (0, –2, -2), (2,3, 4) is

A: A vector orthogonal to the plane through the points (-1,0,0) , (0,-2,-2) , (2,3,4) is

Q: Show that the vectors 3 do not span R° by giving a vector not in their span.

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Q: What is the dimension of the vector space spanned by the vectors v1, v2? v1 = (6, -2, 4) and v2 =…

A: v1 = (6, -2, 4)  v2 = (14, 2,8)  There does not exist any real number c such that v1 = c v2 hence v1…

Q: For vectors ā = (2,4,-1), b =(-1,3,2), calculate the vector projection of b on ā. %3D

A: Vector projection of b→on a→=(a→.b→)a→Consider  a→.b→=(2×(-1))+(4×3)+((-1)×2)…

Q: Find the magnitude of the projection of ⟨-3,-2⟩ onto the vector ⟨1,-2⟩

A: I have appended the formula used in the solution part of the question

Q: | Show that the vectors 2 do not span R³ by giving a vector not in their span.

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Q: a. From the set of vectors{ (1, 2, –1). (-4, –5, –6), (4, 3, 10). (5, –3,2)}. select two pairs of…

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Q: why is it not all 4 vectors span W?

A: Lets look at how span of a set is defined :

Q: Prove that the points position vectors collinear. With at 26, 2a-5 and 3a-46 are

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Q: 4 2. Decide whether the vectors (1, 2,0,-1], [2, 6, -3, -3], [3, 10, -6,-5] are linearly…

A: Given vectors are ,  [ 1,2,0,-1 ] ,  [ 2,6,-3,-3 ] ,  [ 3 ,10 ,-6 ,-5 ]  (.)  The given vectors are…

Q: Find a vector perpendicular to the plane of P(1, 4, 4), Q(2, 4, 5), and R(-3, 4, 0) Which axis on…

A: From the given points we can find two vectors and after that, using the fact that if one vector is…

Q: Find the scalar and vector projections of b onto a. а - (-4, -3), ь - (6, 0) compab projąb

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Q: (2, -3 ,1),(2, -3 ,5) Express the space stretched by the vectors with cartesian equations.

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Q: Find a nonzero vector orthogonal to the plane through P(2,5, 1), Q(-3, 1, –2) and R(5, –3, –1).

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Q: Express the vector (2, –5, 3) in R³ as a lincar combination of the vectors (1.-3, 2), (2, –4, -1)…

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Q: A vector orthogonal to the plane through the points (-1,0,0), (0,0, –2), (2,3, 4) is О О O 6,-10, 3>…

A: Let, Given vectors are P(-1,0,0), Q(0,0,-2) and R(2,3,4). We have to find non zero vector orthogonal…

Q: The length of the vector c = (2, -3, 1) is %3D

A: Length of vector equal to magnitude of that vector  if v = <x,y,z>  then magnitude/Length =…

Q: Determine whether the set of vectors Q={(-1,1,1).(-1,0,2).(1,2,3)} spans R'.

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Q: Find the magnitude of the projection of (- 1, 2) onto the vector (3, 5)

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Q: Suppose {v1, v2, ..., vp} is an orthogoal set of vectors. Show that {c1v1, c2v2, ..., cpvp} will…

A: Since {v1, v2, ..., vp} is an orthogoal set of vectors, dot products between any two of them will be…

Q: Find a nonzero vector orthogonal to the plane through P(2, 5, 1), Q(-3, 1, – 2) and R(5, –3, –1).

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Q: Consider the plane that goes through the point (4, 1, 3) and is orthogonal to vector (2, 3, 1). Is…

A: We know that standard form  for a plane  A(x-x0)+B(y-y0)+C(z-z0)=0  Where (A,B,C) orthogonal vector…

Q: A vector orthogonal to the plane through the points (-1,0,0), (0, – 1, –2), (2, 3, 4) is

A: This could be solve using vector concept.

Q: A vector orthogonal to the plane through the points (-1,0,0), (0, –1, -2), (2, 3, 4) is

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Q: Show that the vectors ( 1, 0,1) ; ( -1, 2,3) and (0, 1; -1) spans R³

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Q: Consider the vectors (2, 1,0, 2], (3, 1,0, 1], [1, 1,0, -1] in R'. Decide whether they independent.…

A: Given: Vectors in ℝ4,                              2,1,0,2, 3,1,0,1, 1,1,0,-1 To find: Whether the…

Q: Find a vector a that has the same direction as (-8, 9,8) but has length 3.

A: The solution is given below

Q: Find a vector perpendicular to the plane of P(1, 4, 4), Q(2, 4, 5), and R(-3, 4, 0). Which axis on…

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