# Differences

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 phy131studiof15:lectures:chapter3 [2015/07/20 15:20]mdawber [Vectors - Components] phy131studiof15:lectures:chapter3 [2015/08/31 09:05] (current)mdawber [Vectors - Components] Both sides previous revision Previous revision 2015/08/31 09:05 mdawber [Vectors - Components] 2015/08/31 08:47 mdawber [Vectors - Multiplication by a scalar] 2015/07/27 16:34 mdawber [Vectors - Multiplication by a scalar] 2015/07/27 16:33 mdawber [Vectors - Components] 2015/07/27 16:21 mdawber [3.P.003] 2015/07/27 16:20 mdawber [3.P.003] 2015/07/27 16:08 mdawber [Adding and subtracting vectors] 2015/07/20 15:20 mdawber [Vectors - Components] 2015/07/20 13:50 mdawber [Adding and subtracting vectors] 2015/07/20 13:48 mdawber created Next revision Previous revision 2015/08/31 09:05 mdawber [Vectors - Components] 2015/08/31 08:47 mdawber [Vectors - Multiplication by a scalar] 2015/07/27 16:34 mdawber [Vectors - Multiplication by a scalar] 2015/07/27 16:33 mdawber [Vectors - Components] 2015/07/27 16:21 mdawber [3.P.003] 2015/07/27 16:20 mdawber [3.P.003] 2015/07/27 16:08 mdawber [Adding and subtracting vectors] 2015/07/20 15:20 mdawber [Vectors - Components] 2015/07/20 13:50 mdawber [Adding and subtracting vectors] 2015/07/20 13:48 mdawber created Line 25: Line 25: {{vectoraddsubstract.png}} {{vectoraddsubstract.png}} + + ===== 3.P.003 ===== + + ===== 3.P.005 ===== ===== Unit Vectors ===== ===== Unit Vectors ===== Line 60: Line 64: {{vectorcomponentadd.png}} {{vectorcomponentadd.png}} + The angles $\theta_{1}$ and $\theta_{2}$ are defined with respect to the positive $x$ axis, ie. $\theta_{1}$ is negative and $\theta_{2}$ is positive. | $v_{1x}=v_{1}\cos\theta_{1}$ <​html>&​nbsp;&​nbsp;&​nbsp;​ | $v_{2x}=v_{2}\cos\theta_{2}$ <​html>&​nbsp;&​nbsp;&​nbsp;​ | | $v_{1x}=v_{1}\cos\theta_{1}$ <​html>&​nbsp;&​nbsp;&​nbsp;​ | $v_{2x}=v_{2}\cos\theta_{2}$ <​html>&​nbsp;&​nbsp;&​nbsp;​ | Line 67: Line 72: | $v_{Rx}=v_{1x}+v_{2x}$ <​html>&​nbsp;&​nbsp;&​nbsp;​ | $\tan\theta_{R}=\frac{v_{Ry}}{v_{Rx}}$ <​html>&​nbsp;&​nbsp;&​nbsp;​ | | $v_{Rx}=v_{1x}+v_{2x}$ <​html>&​nbsp;&​nbsp;&​nbsp;​ | $\tan\theta_{R}=\frac{v_{Ry}}{v_{Rx}}$ <​html>&​nbsp;&​nbsp;&​nbsp;​ | | $v_{Ry}=v_{1y}+v_{2y}$ <​html>&​nbsp;&​nbsp;&​nbsp;​ | $v_{R}=\sqrt{v_{Rx}^2+v_{Ry}^2}$ <​html>&​nbsp;&​nbsp;&​nbsp;​ | | $v_{Ry}=v_{1y}+v_{2y}$ <​html>&​nbsp;&​nbsp;&​nbsp;​ | $v_{R}=\sqrt{v_{Rx}^2+v_{Ry}^2}$ <​html>&​nbsp;&​nbsp;&​nbsp;​ | + + ===== 3.P.027 ===== + + ===== 3.P.042 ===== + + ===== 3.P.051 ===== + + ===== 3.P.062 ===== + + + ===== Vectors - Multiplication by a scalar ===== ===== Vectors - Multiplication by a scalar ===== + + Multiplication of a vector by a scalar can change the magnitude, but not the direction of the vector, ie. each component of the vector is multiplied by the scalar in the same way. + ===== 3.P.071 =====