Suppose the vector ū =<3,1,-47 is translated so that it's heach is at the point C-1,2,3). where ito tail Cst arting point)?

Q: Find a vector å with representation given by the directed line segment AB, for A(0,3,1) and B(2,3, –…

A: We have to find the vector and draw it.

Q: To compute h, (x) =*,+0,x,+0,*, in vectorized form then: (theta vector size is 1x3 and X is 3x1) (A)…

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Q: The vectors u=(1,-2,1), v=(3,0,-2) and w-(5,-4,0) are: O not coplanar coplanar

A: We can check whether the three vectors are co planar  or not as below

Q: Consider the vector v between (-5,5, –3) and (1,1, 1).

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Q: 4. If the projections of vector a on x,y and z −axes are 2,1,2 units respectively, and the angle at…

A: To calculate the angle we use dot product of two vectors given by Taking two vectors as U&amp;V…

Q: What are the conditions for a set of vectors {ai , i ∈ [1, N]} to form a basis for an N dimensional…

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Q: Show that v, = (1,0,–1) , v, = (1,0,1) , v3 = (1,1,1) span R’. %3D Express vector v= (4,2, 2) as…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: The scalar projection of vector A onto another vector B will be the negative of that scalar…

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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: Find a vector that is orthogonal to the plane containing the points. (Orthogonal means…

A: Given points are, P=3,0,1Q=4,-2,1R=5,3,-1 The orthogonal vector n^ will be calculated from the given…

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

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Q: In R³, consider the triangle formed by X (2,0, 4), Y (0,5, 0) and Z (-2,0,0). Us- ing vector and…

A: Let's find.

Q: Find the vector projection of (3, 3, 4) onto (–1, -2, 2).

A: Projection of u onto v is given by.

Q: If a vector u is orthogonal to vectors x and y then u is orthogonal to the vector x + y. :Select one…

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Q: Show that the vectors v, = (0, 3, 1, -1); vz = (6, 0, 5, 1); vz = (4. –7, 1, 3) form linearly…

A: Solve the given problem.

Q: Consider the vector v between (-5, 5, –3) and (1, 1, 1).

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Q: Let a = (7, 10, 1) and b = (10, 3, 6) be vectors. Compute the cross product %3D ахЬ.

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Q: 2. Use a directed line segment to represent the vector. (а) и %3D (2, —4) (b) v = (2,4, –4)

A: Given that the vector a u=2,-4  b v=2,4,-4Solution a u=2,-4u=22+-42u=20  =25b v=2,4,-4v=22+42+-42v=6

Q: Sketch the given vector with initial point (4, 1). u = (-5, 3)

A: Here we have to plot the given vector.

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: Find the moment vector m and m of p = [2,3,0] about Q: (2, 1, 0) acting on a line through A: (0, 3,…

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Q: If a vector u is orthogonal to vectors x and y then u is orthogonal to the vector x+ y. :Select one…

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Q: Suppose di ,de,..do ore distinct real numbecs det Prove ė lineerle fade pendent ere vectors in…

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Q: Decompose the vector ¯b = ⟨1, 0, 4⟩ into its projection proja¯(¯b) and its orthogonal component…

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Q: Express the vector v with initial point P and terminal point Q in component form. P(3, 3), Q(5, 5)

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Q: What is the vector projection of X = (7, 0, – 3) on ỹ = (-1,3,3)? Answer:

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Q: Find two different vector parametrizations of the line through P = (5, 5, 2) with direction vector v…

A: Given the points are (5,5,2) and the direction vector v=&lt;0,-2,1&gt;Hence, Vector…

Q: If ã = <!,2,37 and b=<5,0 -17, find the vector pojection of %3D %3D ŏ onto à.

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

A: I have append the formula in solution part

Q: The vector norm is always positive.(i.e. ||X||>0 for every vector X.) Select one: O True False

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Q: Evaluate The Work Done By The Force Vector, F= (6x^2+3y)I – 15yzj + 10x^2zk From (0,0,0) To (1,1,1)…

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

A: Solution :-

Q: Obtain a Vector of mayni tude lo that has the same direction as the Vector pPerpendicular toiboth 2…

A: The vector here has a magnitude 10 and perpendicular to both the vectors, 2ax⏞-4ay⏞+3az⏞ and…

Q: a' and b Expess the Vector paduct in from of de terminant: 2 = (2, a, as) 5= of where , (6, b, bs)…

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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: Let P be the plane through (1, 2, 3), (4, 3, 3), and (4, 4, 1). Find the vector of length 2 that is…

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Q: 3. What is the initial point of vector w if the component form is and the terminal point is (4, 1)?

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Q: Compute the projection of →a→ onto →b→ and the vector component of →a→ orthogonal to →b→. Let…

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Q: Suppose v is a nonzero position vector in xyz-space. How many position vectors with length 2 in…

A: Given that, v is a nonzero position vector in xyz-space.

Q: Suppose there is a collection of three or more two- dimensional vectors. Provide an argument…

A: Collection of two dimensional vectors mean those vector having i and j components.

Q: Use a directed line segment to represent the vector.u = (−3, −4)

A: The directed  line segment is the vector drawn from the any two points in the cartesian plane. The…

Q: 6. Compute the projections of [1, – 1,0, 1] on the vector [0, 1,0, 2]. |

A: Let v = [1, -1, 0, 1] and u = [0, 1, 0, 2]

Q: Consider the plane that goes through the point (4, 1, 3) I to vector (2, 3, 1).

A: It is given that the plane is passing through the point (4,1,3) and orthogonal to the vector (2,3,1)…

Q: -2 - are the vectors U, = %3D Ug = %3D in M22 are lineor ly depon dent linearly in dependet.

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

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Q: Find the unit vectoru in the di rection of the vectorv=3(2, 2, 1).

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Q: The vector norm is always positive.(i.e. ||X||>0 for every vector X.) Select one: True False

A: We know that The length of a vector with two elements is the square root of the sum of each element…