2003年9月11日 · Components Proofs Vector Vector components In summary, the conversation is about a student struggling with a physics class and needing help understanding vector components. The student is trying to prove the magnitude of a sum vector using components along two perpendicular axes.

2006年12月3日 · Homework Statement Prove that the diagonals of a paraelogram are perpendicular iff the parallelogram is a rhombus. Homework Equations a (dot) b = 0 The Attempt at a Solution This is how I started: By definition, a rhombus is a quadrilateral with all sides equal in length. So this...

2003年12月10日 · In conclusion, vector proofs in geometry can be challenging, but with a systematic approach and practice, you can successfully solve them. Remember to break down the problem into smaller steps, use your knowledge of geometric concepts, and apply vector operations to manipulate the given information.

2013年1月19日 · Proof Vector In summary, we can prove that if a vector $\mathbf{v}(t)$ has a constant magnitude, then its derivative $\dot{\mathbf{v}}(t)$ is orthogonal to $\mathbf{v}(t)$. This can be shown by taking the inner product of $\mathbf{v}(t)$ and its derivative and using the fact that $\mathbf{v}(t)$ has a constant magnitude.

2011年3月7日 · Gradient Gradient vector Proofs Property Vector In summary, the operation of taking the gradient of a function has the given property. The quotient rule for taking the gradient of a quotient of two differentiable functions is given by Δ(u/v) = vΔu - uΔv / v^2.

2012年2月6日 · FAQ: Eigen Vector Proofs: Proving Real Symmetric Matrix M is Positive Definite What is an eigen vector? An eigen vector is a non-zero vector that, when multiplied by a square matrix, gives a scalar multiple of itself. In other words, an eigen vector is a special vector that does not change direction when multiplied by a matrix.

2006年4月8日 · In summary, the conversation discusses working on vector proofs and specifically proving that the diagonals of a parallelogram bisect each other. The conversation also touches on another proof involving parallel lines and their ratios. The final part of the conversation brings up the concept of the triangle inequality.

2008年6月17日 · Example if I had a triangle ABC with midpoints D of BC, E of AC and F of AB. I know G is where the medians intersect. I have seen many proofs and understand the process that proves the addition of the vectors from the centroid to the vertices are zero i.e. GA+GB+GC=0.

2008年10月6日 · Yes, vector proofs for triangles and vector plane questions have many real-life applications in fields such as physics, engineering, and computer graphics. For example, in physics, vectors are used to represent the forces acting on an object and their direction and magnitude can be used to determine the object's motion.

2005年11月11日 · Vector Proofs: A Quadrilateral thing #2! Thanks lightgrav! Search titles and first posts only