# Vector A has a magnitude of 10 and points in the +x direction. Vector B has a magnitude of 16 and makes an angle of 41 with positive x axis. Find A - B

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### 1 Answer

Let's calculate A - B by first calculating its x and y components.

Since A points in x-direction, `A_x = 10` and `` `A_y = 0`

Since B makes angle of 41 degrees with positive x-axis,

`B_x = 16cos41 = 12.075` and `B_y = 16sin41 = 10.497`

Then the components of the difference of two vectors are

`A_x - B_x = 10 - 12.075=-2.075`

`A_y - B_y = 0 - 10.497 = - 10.497`

The magnitude of the difference vector will be

`sqrt((A_x - B_x)^2 + (A_y - B_y)^2) =10.19`

The angle between the difference vector and x-axis will be determined by the equation

`tanalpha = (A_x - B_x)/(A_y - B_y)=5.06` so `alpha = 78.8` degrees. Since both x and y components are negative, the difference angle makes angle -(180 - 78.8) = 101.2 with the positive x-axis.

**Therefore, vector A - B has magnitude of 10.19 and makes angle -101.2 degrees with the positive x-axis.**