Find the value of t for which (4, 6, 3, t) belongs to Span {(1, 3, -4, 1), (2, 8, -5, -1), (-1, -5,0, 2)}

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: Calculate F . dr, where C is the square of (1,1, 1), (–1,1, 1), (-1,–1,1) and (1,–1,1), with…

A: Let F→x,y,z=zex-yezi→+2cosy-xezj→+ex-xyezk→ and C is the square with vertices…

Q: Iculate O F- dĩ, where C is the square of (1,1, 1), (–1, 1, 1), (–1, –1,1) and (1, –1,1), with…

A:

Q: A Bezier curve is defined with 4 control points as bo {0,0}, b = {1,0}, b2 = {2,-2} and bz =…

A: Beizer curve 4 control points as b0=0, 0, b1=1, 0,b2=2, -2, b3 =-2, -2 convert this in the form of…

Q: Find a vector a with representation given by the directed line segment AB. A(0, 4, 2), B(4, 4, –1)…

A: Given vectors

Q: Find a vector a with representation given by the directed line segment AB. A(3, 0, -4), B(3, 4, 4)…

A: The given points are: A3, 0, -4, B3, 4, 4 Vector AB can be represented as vector is AB so the tail…

Q: Find the component of u along v. u - (-2, 4), v- (1//7, 1/v2)

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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…

A:

Q: Find the centroid (ĩ, g) of the triangle with vertices at (0, 0), (10, 0), and (0, 9).

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Q: Let ū = (2, –4), ū = (0, –5), and w = (-5, –3). Find the vector x that satisfies %3D би — о +х — бх…

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Q: Find a vector a with representation given by the directed line segment E A(0, 3, 2), B(5,3, -5) Draw…

A: We need to find the equation from A(0, 3, 2) and B(5, 3, -5).

Q: Find a linear mapping G that maps [0, 1] x [0, 1] to the parallelogram in the xy-plane spanned by…

A: Consider the given figure with the following conditions:

Q: Find a vector a with representation given by the directed → line segment AB, where A(−5, 0, 1) and…

A:

Q: Find the projection of ū = (2, -3, 1) onto v = = (-3, 0, 1) %3D 3 0, А. B. (3.0. -1) В.

A: u→ =2, -3, 1v→ =-3, 0, 1v→ =(-3)2+02 +12       =9+1|v→| =10    u→  · v→ =2, -3, 1·-3, 0, 1u→  · v→ =…

Q: A normal vector to the graph of z = r²y at the point (2, 1, 4) is Select one: (4, 4, 1) О -4, -4, 1)…

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Q: This is for Calc 4, told me to post under advanced math though, please help me solve

A:

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

A: Given vectors v1 = (0, 3, 1, -1); v2 = (6, 0, 5, 1); v3 =(4, -7, 1, 3) . Let c1. v1 + c2. v2 + c3.…

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 projection of u onto v if, u= (4, 2), v = (5, -2).

A: Given, Formula for the projection of u onto v is given by

Q: Let = (0,- 2)v=(3,2) and w=(-2,1) Then the dot product u. (V w) is equal to

A:

Q: Find the shortest distance from the point (1, 5, -5) to the plane 2x + 9y - 3z = 6, using two…

A: Given point is 1,5,-5 and plane is 2x+9y-3z=6

Q: 5) Suppose that the set of vectors {ỉ, 7, w} is linearly independent. Prove that Span({ū, T}) #…

A: Given that u→,v→,w→ is linearly independent. Prove Spanu→,v→≠Spanu→,v→,w→.

Q: Find the vector from the origin to the point of intersection of the medians of the triangle whose…

A: To determine the point of intersection of the medians of the triangle.

Q: The vectors in Z22 are [ O, O] , [ O, l], [l, O ], and [l, l ]. (How many vectors doesZn 2 contain,…

A:

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: 9. Let A=span{v = (-1,–1,2), i = Projau. (2,3,0)} and w (1,2, 3). Find

A:

Q: find the projection of u along v u = (2, 5), v = (1, 1)

A: u=2,5 and v=1,1

Q: Find a linear mapping G that maps [0, 1] × [0, 1] to the parallelogram in the xy-plane spanned by…

A: According to the given information, it is required to find a linear mapping G.

Q: Defined byT (x, y, z) = (y+2z, –2x+y+2z, –3x– y+52), is diagonalizable.

A:

Q: Find orthogonal projection of u=(-1, 2, 5) in the direction of v=(3, 1, -2).

A: find the orthogonal projection of u=-1,2,5 in the direction of vector v=3,1,2 it is known that…

Q: A point moves so that sum of the squares of its distances from the vertices of a triangle is always…

A:

Q: Find the projection of u along v. u =〈2, -3〉, v =〈1, 2〉

A: Given: u =〈2, -3〉, v =〈1, 2〉 To find the projection of u along v

Q: Find all the planes parallel to the plane passing through the points(1, 2, 3), (1, 2, 7), and (1, 1,…

A:

Q: What is the maximum of || Ar||∞ if ||r||∞ = 1? What is the maximum of ||Ar||2 if |-|2 = 1? For…

A: A=2123 (a) We know that Ax∞≤max∑ka1k,∑ka1k,…∑ka1k when x∞=1. Ax∞≤max2+1,2+3=5 The maximum of Ax∞ is…

Q: FIR R whose by (1,213) qnd (4,5,6) a) Find Iinear mapping Image is generated

A: NOTE: According to guideline answer of first question can be given, for other please ask in a…

Q: Let L, be the line passing through the point P-(1, -7, 5) with direction vector d-[1,-2, 0], and let…

A:

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 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: 8) Rectangle GHJK with vertices G(2,3), H(2, 5), J(6, 5) and K(6, 3) is rotated 180° about the…

A:

Q: Find a vector n perpendicular to the plane determined by the three points A(1, -1,2), В(2, 0, — 1)…

A: Given three points ( position vectors) are; A( 1,-1, 2) , B( 2,0,-1) and C(0, 2,1)

Q: Find the particular number of orthogonal transectories of x2+cy2=1 passing through the point (2,1)

A: Given equation is x2+cy2=1........1. We have to find the particular number of orthogonal…

Q: Find scalars a, b, csuch that au + bv + cw = = (-6,12,4) u = (-1,0,2), v = (2,2,–2), w = (1,–2,1)

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Q: Next question Costruct a glide refection of tiangle ABC using vector v and reflection lineL Choose…

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Q: Find the vector v in the plane represented by the directed line segment from (4,-3) to (-2,6)

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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).

A:

Q: Find orthogonal projection of v=(3, 1, -2) in the direction of u=(-1, 2, 5).

A:

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: Find a vector a with representation given by the directed line segment AB. А(О, 3, 2), в(1, з, -5)…

A: Consider the given line segment AB→. A(0,3,2) and B(1,3,-5). Let AB→ be  a vector from A to B and…

Q: Find a vector a with representation given by the directed line segmer (-6,0, 3) and B(1,8, –1).

A:

Q: The normal vector of 2x + 3y - z + 5 = 0 is: O [3, -1, 5] O [2, 3, -1] [2, 3, -1, 5] O (-2, -3, 1]

A: Answer :  From question given that the Normal vector form is  ; 2x + 3y - z + 5 = 0

Family of Curves

A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.

XZ Plane

In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.  

Euclidean Geometry

Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.

Lines and Angles

In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.