东南大学：《建筑力学 Architectural Mechanics》课程教学课件（英文讲稿）A02 Statics of Particles

Addition of VectorsTrapezoidruleforvectoraddition?Triangle rule for vector additionP+OA? Law of cosines,QR2 = P2 +Q?-2PQcos BBR=P+QOQLawof sinesQP+ACsin BsinCsin A(a)PRQBQAG(b). Vector addition is commutative,P+0=0+P-.Vectorsubtraction(b)(a)6

Addition of Vectors • Trapezoid rule for vector addition • Triangle rule for vector addition B B C C R P Q R P Q PQ B         2 cos 2 2 2 • Law of cosines, • Law of sines, sin sin sin ABC Q R P   • Vector addition is commutative, P Q Q P        • Vector subtraction 6

Addition of Vectors.Addition of three or more vectors throughrepeated application of the triangle ruleQ+SP+Q+S. The polygon rule for the addition of three ormorevectors.Vector addition is associative,P+Q+SP+Q+S=(P+@)+S=P+@+S1.5P. Multiplicationof a vectorby a scalar2P7

Addition of Vectors • Addition of three or more vectors through repeated application of the triangle rule • The polygon rule for the addition of three or more vectors. • Vector addition is associative, P Q S P Q S P Q S                  • Multiplication of a vector by a scalar 7