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Mathematics - Proof of Midpoint Theorem using Vectors.The midpoint of a side of a triangle in R^3 is the point that bisects that side (i.e., that divides it in
Vectors: Resultant Vector.Two students are using ropes to pull on a heavy object, as shown in the diagram below.
Equation of a plane.Specify the area of the triangle defined by p1, p2, and p3.
Linearly dependent set of three vectors. What is an example of a linearly dependent set of three vectors with the property that any single vector
Linear combination of the given vectors. Suppose {v_1, v_2, v_3} is linearly independent set of vectors in R^n.
Translation and reflection. A student claims that anything that can be accomplished by a translation can be accomplished by a reflection
Find a unit vector n perpendicular to the plane through the points P(1, 3, -2), Q(2, 4, 5), and R(-3, -2, 2).
Component form of the vector.Find the component form of the vector v that has an initial point at (1,-2,2) and a terminal point
Normal and binormal vectors to a curve and normal plane. If C is the curve given parametrically by R(t)=cost(i)+sint(j)+2t(k) find
Write a plane equation for plane passing through P (1,2,3) and perpendicular to n = .
Projecting a vector.Let C^3 be equipped with the standard inner product and Let W be the subspace of C^3 that is spanned
Find the volume of the parallelpipe with adjacent edges a,b,and c.Determine if the vectors a and b are parallel, perpendicular or neither.
The surface integral of the normal component of curl F over the open hemispherical surface (x^2)+(y^2)+(z^2)=4 above the xy plane
Briefly explain, which of the following are vector spaces? (a) The set of all real symmetric 3x3 matrices.
Convergent subsequences.If A and U are two subsets of a normed vector space, and U is open, show that A+U is open.
Simultaneous vector equations.Solve the simultaneous vector equations for r:r x a=b, r â?¢ c=a, given that a â?¢ b=0
The equation of a plane.Are these statements true or false and please explain why.
Let V be the vector space of all functions f: R ?R. Determine whether the following subsets of V form subspaces.
Vector Space basis.which of the following is a basis for P_2?
Vertex, axis, domain and range.The math problems and descriptions are in the word document.
Vector analysis. In R^n with the standard inner product, consider the vector.
Determine if the set R^2 (the real plane) is a vector space with operations defined by the following:
Properties of Vector Spaces. Please write complete, formal and professional proofs for your answer.
Subspaces of the Vector Space of 2-by-2 Matrices. Please use formal proofs and language where applicable, and be sure to explain your reasoning thoroughly.
Writing a_1,a_2,b as column vectors. Suppose L_1 is the line through the origin in the direction of a_1, and L_2 is the line through b in the direction of a_2.