Please help with math problems?

Question

Calculate perimeter of a triangle ABC with coordinates A ( 0,-1) B (-8,7) C(4,2) (use vectors)

In this triangle calculate length of medians and transversal
Find opposite vector to a(5,12) b(-1,40)
calculate s= a+b
r= a-b

Given are vectors a, b. Find out wether they are linearly dependend or inedepended
a= (-3,-4) b= AB A (-5,7) B(-8,8)

Given is vector u. Find vector v so that u.v=0
u= (6,-9) v=(v1,72)
Thank you very very much!

Answer 1

I'll do some of this.

Part 1. Vector AB = -8i + 8j (magnitude 8 sqrt 2)
Vector AC = 4i + 3j (magnitude 5)
Vector BC = 12i - 5j (magnitude 13)
Perimeter = sum of magnitudes = 18 + 8 sqrt 2

The median of a triangle goes from a vertex to the midpoint of the opposite side. You can do that. Also, I don't know what transversal you're talking about.

Part 2. I assume you mean a = 5i + 12j and b = -i + 40j
I don't know what the "opposite vector" means.

s = a + b = 4i + 52j
r = a - b = 6i - 28j

Part 3. I guess you mean a = -3i - 4j and b = -3i + 2j
These are linearly independent because one is not a multiple of the other.

Part 4. u dot v = 6 v1 - 9(72) = 0
v1 = 9(12) = 108
v = (108, 72) in your notation.

Answer 2

Well, I am not the best at math at the moment

Answer 3

hmmmmmmmmm......... i dont know