2. Find projection(A,B)
`A=(3,4)`,`B=(4,3)`,`C=(3,4)`
Solution:
Here `vec A=(3,4),vec B=(4,3),vec C=(3,4)`
`proj_(vec B)vec A=(vec A * vec B)/|vec B|^2 * vec B`
1. Calculate dot product
`vec A * vec B`
`=A_1*B_1 + A_2*B_2`
`=3*4 + 4*3`
`=12 + 12`
`=24`
2. Calculate magnitude
`|vec B|`
`=sqrt(B_1^2 + B_2^2)`
`=sqrt(4^2 + 3^2)`
`=sqrt(16 + 9)`
`=sqrt(25)`
`=5`
`:.|vec B|^2=25`
The Vector projection is given by
`proj_(vec B)vec A=(vec A * vec B)/|vec B|^2 * vec B`
`=(24)/(25) * vec B`
`=(24)/(25) * (4,3)`
`=(3.84,2.88)`
The scalar projection is given by
`proj_(vec B)vec A=(vec A * vec B)/|vec B|`
Now, `(vec A * vec B)/(|vec B|)`
`=4.8`
This material is intended as a summary. Use your textbook for detail explanation.
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