# Vectors help

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1. Dec 4, 2014

### sarabee

1.
If u=-7i-3j and v=-4i+4j, find w=5u+4v.

2. I'm not sure which equation to use? Test is tomorrow so fast help would be great!

3. The attempt at a solution: So my teacher gave us the answer key and it reads: -51i+j and i am not sure how to get that?? Please help!

2. Dec 4, 2014

### Staff: Mentor

Try plugging in the the u and v vectors into the w equation and regroup adding like terms ie the i terms and the j terms.

3. Dec 4, 2014

### sarabee

Thanks! Just solved & it makes perfect sense.
While I have you here, i might as well ask another question:
Find the magnitude and direction angle of v=2i-2j. Round direction angle to nearest degree.
not sure how to get that!

4. Dec 4, 2014

### sarabee

I'm not sure how to tag you but.. i'm just going to try this

5. Dec 4, 2014

### Staff: Mentor

If you draw the vector on graph paper you'll see it makes a triangle with the x-axis.

so how would you determine the angle between the vector and the x-axis using trig

for the magnitude, you're familiar with the pythagorean theorem right?

6. Dec 4, 2014

### sarabee

so...would the point just be <2,-2> then? and i just don't understand at all how to graph a triangle given only one point

and yes i am familiar with the pythag theorem

7. Dec 4, 2014

### Staff: Mentor

You have a vector so place its tail at 0,0 and now you have a triangle

8. Dec 4, 2014

### sarabee

http://imgur.com/OhURuK8
So this is the triangle i have now
http://imgur.com/OhURuK8 if you cant see that image. what do i do next?

9. Dec 4, 2014

### Staff: Mentor

Review your notes on vectors this is a very simple problem and I've given you enough hints. You see the triangle and you must know trig, the hypotenuse length is the magnitude of the vector.

10. Dec 4, 2014

### sarabee

Thanks for all your help, I have it figured out for the most part.
When i am using trig to solve for a direction angle, which one am i solving for? the one that is nearest to (0,0)? or the other one?
http://imgur.com/PwVyw6S

11. Dec 4, 2014

### Staff: Mentor

The angle with 0,0 are the vertex.

I noticed in your scribbling you said 2 squared + 2 squared = 16 are you sure that adds up right?

12. Dec 5, 2014

### Staff: Mentor

This problem is less about what equation to use, but more about 1)how two add two vectors, and 2) how to multiply a vector by a scalar.

If you spend your time trying to memorize equations without any understanding, you won't do well on a test.