Calculating 2A + 3(B+C): Vector Addition

[klm]

vector A= (2,-1,1)
vec. B = ( 3, 0, 5)
vec. C = (1,4,-2)
what is 2A + 3(B+C)

this is what i did:
2A = 2(2,-1,1) = (4,-2, 2)

(B+C) = (4,4,3) x 3 = (12,12, 9)

2A + 3(B+C) = (16,10,11)

is this the correct way to think and do this problem?

 

[bel]

Yes, you just add up the components because all vectors are the sum of their components; and of course, a scalar times a vector is just a vector of scaled up magnitude in the direction of the original vector.

 

[klm]

okay thank you! and is it all right to multiply like that? or is there some other rule for multiplying vectors?

 

[bel]

It is all right, because that is just a case of a scalar multiplying a vector.

 

[klm]

ok! thank you very much!