shows the following three vectors:
`veca = (4.2 m) hati - (1.5 m) hatj,`
`vecb = (-1.6m) hati + (2.9 m) hatj,`
and ` vecc = (-3.7m) hatj.`
What is their vector sum `vecr` which is also shown ?

Explanation

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.