Question

If u = <-7, 6> and v = <-4, 17>, which vector can be added to u + 3v to get the unit vector <1, 0> as the resultant vector?

Answer 1

With u = <-7, 6> and v = <-4, 17>, we have

u + 3v = <-7, 6> + 3 <-4, 17> = <-7, 6> + <-12, 51> = <-19, 57>

We want to find a vector w such that

u + 3v + w = <1, 0>

Subtract u + 3v from both sides to get

w = <1, 0> - (u + 3v) = <1, 0> - <-19, 57>

w = <20, -57>