Calculate the unit vector (in terms of i(hat) and j(hat) ) in the direction opposite to the direction of each of the following vectors. Vector A= 3.7i(hat) + 4.5j(hat)

Question

ash2326 · Answer

@Bakken2012 could you find the unit vector for A?

anonymous · Answer

no im confused on how to do it

ash2326 · Answer

Ok, I'll explain you

ash2326 · Answer

Unit vector is a vector with magnitude 1
suppose A' is a unit vector
$$A'=ai+bj$$
then 
$$\sqrt{a^2+b^2}=1$$
If we have a vector B=ci+dj
B is not a unit vector, but a unit vector in direction of b would be
$$\frac{ci}{\sqrt{c^2+d^2}} \ \ \ \ \ \  \ \ \ \ +\frac{dj}{\sqrt{c^2+d^2}}$$
do you understand this?

anonymous · Answer

ok i understand that, but i beleive I am supposed to calculate it in the opposite direction

ash2326 · Answer

Yeah, unit vector in opposite direction is
$$-\frac{ci}{\sqrt{c^2+d^2}} \ \ \ \ \ \  \ \ \ \ -\frac{dj}{\sqrt{c^2+d^2}}$$

anonymous · Answer

ok

ash2326 · Answer

@Bakken2012 could you do it now?

anonymous · Answer

i think so let me try

ash2326 · Answer

cool :)

phi · Answer

in pictures:
|dw:1347991286042:dw|