Find two vectors v1 and v2 whose sum is <-3,3> , where v1 is parallel to <-1,0> while v2 is perpendicular to <-1,0>

Answer 1

Let's let v1 = <a,b>, and v2 = <c,d>

v1 + v2 = <a+c, b+d> = <-3, 3>

a+c = -3

b+d = 3

Draw <-1, 0> and you see that it is horizontal. Any vector parallel will also be horizontal and have 0 for it's y value.

So, b = 0

Likewise, any vector perpendicular to <-1, 0> will be vertical and have 0 for it's x value.

So, c = 0

a and d follow