Question

How do you find a) u+v, b) u-v, c) 2u-3v given `u=<0,0>, v=<2,1>`?

Answer 1

`((2),(1)),((-2),(-1)),((-6),(-3))`

Explanation:

`"Note the notation " <0,0>" is equivalent to " ((0),(0))`

Add/subtract corresponding x and y components from each vector.

`rArrulu+ulv=((0),(0))+((2),(1))`

`color(white)(xxxxxxx)=((0+2),(0+1))=((2),(1))`

`rArrulu-ulv=((0),(0))-((2),(1))`

`color(white)(xxxxxxx)=((0-2),(0-1))=((-2),(-1))`

multiply each x and y component by the scalar quantity.

`rArr2ulu-3ulv=2((0),(0))-3((2),(1))`

`color(white)(xxxxxxxxx)=((2xx0),(2xx0))-((3xx2),(3xx1))`

`color(white)(xxxxxxxxx)=((0),(0))-((6),(3))=((-6),(-3))`