Could you please help with vectors

If a = 3i - j +2k & b = 2i - 2j + 4k
find a+b, a-b, a・b, and a×b.
Thank you for your help,
Could you please show step by step?

a+b
what you do here is just adding the different components individually:
(3+2)i + (-1-2)j + (2+4)k=5i - 3j + 6k

a-b
just subtract the components individually
(3-2)i + (-1-(-2))j + (2-4)k = i + j - 2k

skalar (dot) product
you can find the pattern in any good collection of formulae used in math or physics
the pattern:
assume
a=(a_1, a_2, a_3)
b=(b_1, b_2, b_3)
then
a・b is then (a_1*b_1)i + (a_2*b_2)j + (a_3*b_3)k

in other words
a・b = (3*2)i+((-1)*(-2))j + (2*4)k = 6i + 2j + 8k

vector (cross) product
same here, if you don't know the formula by heart, find it somewhere (knowing it by heart is overkill, dont waste your time trying to learn it unless you need really need to)
a×b = (a_2*b_3 - a_3*b_2)i + (a_3*b_1 - a_1*b_3)j + (a_1*b_2 - a_2*b_1)k

so putting in the numbers one gets:
a×b = ((-1)*4 - 2*(-2))i + (2*2 - 3*4)j + (3*(-2) - (-1)*2)k = 0i - 8j - 4k