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shows the following three vectors: veca = (4.2 m) hati - (1.5 m) hatj, vecb = (-1.6m) hati + (2.9 m) hatj, andvecc = (-3.7m) hatj. What is their vector sum vecr which is also shown ? |
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Answer» Solution :For x axis, we add the x components of `veca, VECB and vecc` to get the x component of the vector sum `vecr:` `r _(x) = a _(x) + b _(x) + c_(x)` `= 4.2 m - 1. 6m + 0= 2.6 m.` Similarly, for the y axis, `r _(y) = a _(y) + b _(y) + c _(y)` `=-1.5 m + 2.9 m - 3.7 m =-2.3m.` We then combine these components of `vecr` to write the vector in unit-vector notation: ` vecr = (2.6m ) hati - (2.3 m) hatj,` where `(2.6m)hati` is the vector component of `vecr` along the x axis and `- (2.6 m) hatj` is that along the y axis. shows one way to arrang ethese vector components to from `vecr.` (Can you sketch the other way?) We can also answer the equation by GIVING the magnitude and an angle for `vecr.` the magnitude is `r = sqrt ((2.6m) ^(2) + (-2.3 m) ^(2))~~ 3.5 m` and the angle (MEASURED from the + x direction) is `theta = tan ^(-1) ((-2.3 m)/( 2.6m)) =- 41 ^(@),` where the minus SIGN means clockwise. 
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