Vector Calculus : Deriving the Law of Sines and Volume of a Parallelepiped Using the Triple Scalar Product

Related BrainMass Solutions

• Volume of a parallelepiped and vectors

  62570 Volume of a parallelepiped and vectors A parallelepiped is defined by the three non-collinear vectors A, B, C.

• Planes & Vectors : Points and Equations of Parallel Lines

  The volume of this parallelepiped (is the product of area of the base and altitude) is equal to the scalar triple product u.(v x w). If the points all lie in one plane, then u.(v x w) = 0 Now, v x w = = (0, 0, 4-a) u.

• Calculus - Vectors - Area of Triangle, Volume of Parallepipe

  The solution to the posted problems in Calculus on Vector Product, Finding Area of Triangle, Finding Orthogonal Vector to a Plane, Finding Area of Parallelopiped using vectors are given with step by step explanation with all the procedure and working

• Vector Calculus, Partial Derivatives, and Polar Cylindrical and Spherical Coordinates

  524122 Vector Calculus, Partial Derivatives, and Coordinates See the attached file. Vectors 1. The points A(2; -3, 3), B(3,5;4), C(3;8;-2) and D(4;4;6) are vertices of a tetrahedron. Find the volume of the tetrahedron. 2.

• Scalar and Vector Products

  31719 Scalar and Vector Products We have three vectors: A = i + 2j ; B = 2j + k ; C = 2i + k a. Find the scalar triple product by direct multiplication. and b. The vector triple product by direct multiplication. a. (i) A ? B à?

• Coding in Matlab - Dot, cross, and triple products

  524121 Coding in Matlab - Dot, Cross, and Triple Products See the attached file. The objective is to write MATLAB codes that calculate scalar, vector and triple (scalar) products of vectors.

• Flowing water: Volume of water that flows through this surface per unit time is equal to flux

  algebra that the flux is determined by a dot product (scalar product) The solution explains and provides all the calculations in arriving at the answer, together with a graph.

• Vector Calculus Principle Normal Vector and Binomial Vector

  dB/dt = a N + b B = a N dB/dt = a N We have shown that dB/dt is a scalar multiple of N. I have used vector calculus to prove the given identities. Solution is in a 2-page word document.

• Volume of the parallelepiped

  344143 Volume of the Parallelepiped Calculate the given quantities if a = <1,1,-2>, b= <3,-2,1>, and c=<1,1,-5>. a) 2a + 3b b) |b| c) Unit vector in the direction of b.