Help with vector angle and magnitude

[BlinkBunnie069]

1.
Two Vectors Three Here are two vectors:
a = (6.0 m)i - (3.0 m)j and b = (5.0 m)i + (5.0 m)j.
(a) What is the magnitude of a?

(b) What is the angle of a(relative to i)?

(c) What is the magnitude of b?

(d) What is the angle of b?

(e) What is the magnitude of a + b?

(f) What is the angle of a + b?

(g) What is the magnitude of b - a?

(h) What is the angle of b - a?

(i) What is the magnitude of a - b?

(j) What is the angle of a - b?

(k) What is the angle between the directions of b - a and a - b?
The angle between the two vectors is 180°.
The angle between the two vectors is 90°.
The angle between the two vectors is 60°.
The angle between the two vectors is 30°.
The angle between the two vectors is 45°.
The angle between the two vectors is 0°.

I have no idea how to figure out the magnitude, I thought I did but I only confused myself more. If someone can tell me how to find the magnitude how they want me to find it and also the angle, if would be appreciate. Thanks!

 

[asd1249jf]

1.
Two Vectors Three Here are two vectors:
a = (6.0 m)i - (3.0 m)j and b = (5.0 m)i + (5.0 m)j.
(a) What is the magnitude of a?

(b) What is the angle of a(relative to i)?

(c) What is the magnitude of b?

(d) What is the angle of b?

(e) What is the magnitude of a + b?

(f) What is the angle of a + b?

(g) What is the magnitude of b - a?

(h) What is the angle of b - a?

(i) What is the magnitude of a - b?

(j) What is the angle of a - b?

(k) What is the angle between the directions of b - a and a - b?
The angle between the two vectors is 180°.
The angle between the two vectors is 90°.
The angle between the two vectors is 60°.
The angle between the two vectors is 30°.
The angle between the two vectors is 45°.
The angle between the two vectors is 0°.

I have no idea how to figure out the magnitude, I thought I did but I only confused myself more. If someone can tell me how to find the magnitude how they want me to find it and also the angle, if would be appreciate. Thanks!

Draw the vector on a graph paper. Draw a line 6 units to the right, 3 units downwards, then use the head-to-tail rule to draw the magnitude of a (It should be a diagonal line). That is your graphical representation of the vector you have.

Notice if you do that, you have a right triangle, with the hypotenuse being your magnitude. What rule do you use to find the hypotenuse of a right triangle, if you know the length of two other sides?

 

[BlinkBunnie069]

You use tan= opp./adj to find the hypotenuse I believe. I haven't had much experience w/ trig. So for a) it would be 6/3= 3m and for b) 5/5=1. Am I on the right track?

Now for the angle of a(relative to i), would I take the inverse tangent of 3? Or how would this part work?

Also the magnitude when adding the two different vectors, I'm not sure how you would solve for them when you'd have 4 different values from a and b. Actually, would you just add and subtract the two values you solve for in parts a and b for parts e, g, and i?

 

[asd1249jf]

You use tan= opp./adj to find the hypotenuse I believe. I haven't had much experience w/ trig. So for a) it would be 6/3= 3m and for b) 5/5=1. Am I on the right track?

Now for the angle of a(relative to i), would I take the inverse tangent of 3? Or how would this part work?

Also the magnitude when adding the two different vectors, I'm not sure how you would solve for them when you'd have 4 different values from a and b. Actually, would you just add and subtract the two values you solve for in parts a and b for parts e, g, and i?

You are making this more complicated than it should be.

Suppose you know the sides of b,a. What rule can you use to find c?

As for adding the magnitude of two different vectors, you use the similar idea, except you add the corresponding components together, and use the rule mentioned above to calculate the magnitude.