Solve for w: u=-7i-3j, v=-4i+4j, w=5u+4v

[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!

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![/B]

 

[jedishrfu]

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.

 

[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.
Answer is llvll=2radical2 and theta=315deg
not sure how to get that!

 

[sarabee]

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.

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

 

[jedishrfu]

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?

 

[sarabee]

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?

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

 

[jedishrfu]

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

 

[sarabee]

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

http://imgur.com/OhURuK8
So this is the triangle i have now
http://imgur.com/OhURuK8 if you can't see that image. what do i do next?

 

[jedishrfu]

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.

 

[sarabee]

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.

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

 

[jedishrfu]

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?

 

[Mark44]

2. I'm not sure which equation to use?

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.