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This Lesson (Sum of vectors connecting the center of mass of a triangle with its vertices) was created by by ikleyn(52781)
  About ikleyn: Sum of vectors connecting the center of mass of a triangle with its verticesProve yourself that for any triangle in a plane the sum of the vectors connecting the center of mass of the triangle with its vertices is equal to zero. In a coordinate plane, the center of mass of a triangle with vertices P=P(x1,y1), Q=Q(x2,y2) and R=R(x3,y3) is the point with the coordinates The center of mass of a triangle is called sometimes a centroid or a barycenter of the triangle. Tip: Use the component form of vectors in a coordinate plane (see the lessons Vectors in a coordinate plane and Addition, Subtraction and Multiplication by a number of vectors in a coordinate plane under the topic Introduction to vectors, addition and scaling of the section Algebra-II in this site). If you want to see this Problem solved, find the solution in the lesson Sum of vectors connecting the center of mass of a n-sided polygon with its vertices under the topic Introduction to vectors, addition and scaling of the section Algebra-II in this site. Note. For any triangle, the center of mass coincides with the intersection point of the triangle's medians. This is proved in the lesson The Centroid of a triangle is the Intersection point of its medians under the topic Geometry of the section Word problems in this site. My introductory lessons on vectors in this site are - Vectors in a plane - Sum of vectors that are coherently oriented sides of a convex closed polygon - Sum of vectors that are coherently oriented sides of an unclosed polygon - Sum of vectors that connect the center of a parallelogram with its vertices - Vectors in a coordinate plane - Addition, Subtraction and Multiplication by a number of vectors in a coordinate plane - Summing vectors that are coherently oriented sides of a convex closed polygon - Summing vectors that are coherently oriented sides of an unclosed polygon - The Centroid of a triangle is the Intersection point of its medians - The Centroid of a parallelogram is the Intersection point of its diagonals - Sum of vectors connecting the center of mass of a triangle with its vertices (this lesson) - Sum of vectors connecting the center of mass of a quadrilateral with its vertices - Sum of vectors connecting the center of mass of a n-sided polygon with its vertices - Sum of vectors connecting the center of a regular n-sided polygon with its vertices - Solved problems on vectors in a plane - Solved problems on vectors in a coordinate plane - HOW TO find the length of the vector in a coordinate plane - Flying airplane, blowing wind, airspeed, groundspeed etc. - OVERVIEW of Introductory lessons on vectors in a plane Use this file/link ALGEBRA-II - YOUR ONLINE TEXTBOOK to navigate over all topics and lessons of the online textbook ALGEBRA-II. This lesson has been accessed 3817 times. |
