precalculates vectors

Question

Let v=(-1,4) and w=(3,-2) Find:

 

i.) llvll

ii.) 2v-3w

iii.) ll2v-3wll

iv.) The unit vector u, in the direction of v

 

Do not graph 

Answer 1

Greetings! Lets solve this shall we ?

So, we must find each answer for i), ii), iii) and iv) such that i) yields the magnitude of vector v such that

i) ||v|| = √(-1)²+(4)² = √(17)...........Then ii) yields 2v - 3w such that

ii) 2v - 2w = 2<-1,4> - 3<3, -2> = <-2, 8> - <9, -6> = <-11, 14> ............Then iii) yields the magnitude of 2v-3w such that

iii) ||2v-3w|| = √(-11)²+(14)² = √(317)............Then we find the unit vector u in the direction of v such that

iv) u = v / ||v|| = <-1, 4> / √(17) = - (√(17) / 17)i + (4√(17) / 17)j

I hope this helped!