Vector Geometry, Cross Products and Real Inner Products

Please see the attached file for the fully formatted problem. 1. Write the vector equation of the line in R^3 which passes through the two points P: (1,-1,3) and Q: (2,-1,-1). Show work. Help: R^3: is Euclidean 3-space

Vector Geometry, Cross Products and Real Inner Products: Moorean 3-Space

Please see the attached file for full problem description. 1. Demonstrate (check the properties) that the following function is an inner product in R^3. (Call R^3 with this inner product Moorean 3-space). Let u=(u_1,u_2,u_3) and v=(v_1,v_2,v_3). Then = uAv^T, where A=[ 2 0 0 ] [ 0 1 0 ] [ 0 0 2 ]. Show work. Help: [ 2 0 0 ] [ 0 1 0 ] : is a 3 x 3 matrix. [ 0 0 2 ]

Vector geometry, cross products, and real inner products; Moorean 3-space

Please see the attached file for full problem description.

Vector geometry, cross products, and real inner products.

Please see the attached file for full problem description. 1. Let p_1=3-4x and p_2=3x+4x^2 be vectors (polynomials) in P_2. Use the integral inner product from 0 to 1 to find . Show work.

Vector geometry, cross products, and real inner products.

Please see the attached file for full problem description. Prove that if u and v are given non-zero vectors in the arbitrary inner-product space V, and are such that =0, then {u,v} is a linearly independent subset of V. Show work.