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Component of vector A along the direction of B

Component of vector A along the direction of B. A. Project A onto B: Drop perpendiculars to B. This component is positive. B. A. This component is negative. B. Sometimes only one perpendicular needs be dropped:. A. B. Weight of object on an incline. Choose B to point down incline. B.

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Component of vector A along the direction of B

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  1. Component of vector A along the direction of B A Project A onto B: Drop perpendiculars to B This component is positive B A This component is negative B

  2. Sometimes only one perpendicular needs be dropped: A B Weight of object on an incline Choose B to point down incline B A

  3. Special Cases A 5 Component = +5 B 5 B A Component = -3 3 3 A Component = 0 B

  4. X- and y- components y A Ay x Ax

  5. How to calculate components A 1. Make component part of a triangle containing A 5 2. Identify an angle in the triangle x 3. Use trig to find length of component: sine or cosine? Adjacent. Therefore cosine. Length of component =5cos30°=5×0.866=4.33 4. Add appropriate sign: X-Component = - 4.33

  6. How to calculate components A 1. Make component part of a triangle containing A 5 2. Identify an angle in the triangle 5 x 3. Use trig to find length of component: sine or cosine? Opposite. Therefore sine. Length of component =5sin60°=5×0.866=4.33 4. Add appropriate sign: X-Component = - 4.33

  7. Component of sum=sum pf components y Cx=Ax+Bx B C=A+B A Cy=Ay+By x Cx Bx Ax

  8. Reconstructing a vector from its components y Ay=-4 Ax=3 1. Draw x and y axis 2. Go 4 units in positive x direction 3 x θ 3, Then go 3 units in negative y direction 4 A 4. Join origin to end point

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