Question

Let v1=(2,-6) and v2= (-4,7)

a. compute |v1| and |v2|.

b. compute the unit vectors in the direction of |v1| and |v2|.

c. Draw and lable v1,v2, v1+v2


plz help if you can :)

Answer 1

Magnitude of a vector \(\vec a = (a_1,a_2)\) is given as follows by the Pythagorean theorem:\[|\vec a|=\sqrt{a_1^2+a_2^2}\]The unit vector \(\hat a\) of \(\vec a\) is given as follows.\[\hat a = \frac{\vec a}{|\vec a|}\]This is essentially scaling the original vector \(\vec a\) down by its length so it retains its direction, but has magnitude 1. The following will help you with c, which visualizes vector addition: http://mathworld.wolfram.com/images/eps-gif/ParallelogramLaw_1000.gif