Find unit vetors satisfying qualifying conditions HELP test tomorrow

[darthxepher]

Find unit vetors satisfying qualifying conditions! HELP test tomorrow

Homework Statement

Find the unit vectors satisfying qualifying conditions:

a. oppositely directed to 3i-4j

b. same direction as 2i-j-2k

c. same direction as vector from A(-3,2) to B(1,-1)




Thoughts.
Ok. So i don't know where to start. Can someone hint me. I know to find unit vector u must divide each term by the magnitude but the direction stuff isn't helping me. lol

 

[gabbagabbahey]

Call the unit vector $\hat{n}=n_1\hat{i}+n_2\hat{j}+n_3\hat{k}$ and look at what your conditions tell you about $\hat{n}$...

(a) directed oppositely to 3i-4j...what is the direction of 3i-4j...what does that mean the direction of $\hat{n}$ is?...remember $\hat{n}$ is a unit vector, so you know its magnitude is 1.

(b)same direction as 2i-j-2k...what IS the direction of 2i-j-2k?

(c)what is the vector from A to B?...what is its direction?

 

[darthxepher]

Ok. I kinda figured it out. Thanks for the help... But can u check ur answers with me.

Here are my answers.

a) (-3/5)i + (4/5)j

b) (2/3)i - (1/3)j - (2/3)k

c) (4/5)i - (3/5)j

Thanks for your time!

 

[gabbagabbahey]

Looks good to me!