Question

In general it is best to conceptualize vectors as arrows in space, and then to make calculations with them using their components. (You must first specify a coordinate system in order to find the components of each arrow.) This problem gives you some practice with the components. Let vectors
A =(1,0,−3), B =(−2,5,1), and C =(3,1,1). Calculate the following, and express your answers as ordered triplets of values separated by commas.

a. A- B=______
b. B-C=_______
c. -A +B- C=______
d. 3A- 2C=______
e. -2A+3B- C=_____
f. 2A- 3(B-C)

Answer 1

Answer:

a)A-B =(1,0,-3) +(2,-5,-1) =(3, -5, -4);    

b)B-C =(-2-3, 5-1, 1-1) = (-5,4,0);  

c)-A +(B –C) = (-1,0,3) +(-5,4,0) =(-6,4,3);  

d) =(3,0,-9) –(6,2,2) = (-3, -2, -11);  

e) = (-2,0,6) +(-6,15,3) +(-3,-1,-1) =

d) = (2,0,-6) –(-5*3, 4*3, 0) =  

Explanation:

1)C=k*A = (k*a1, k*a2, k*a3);

2)C=-A = -1*A;

3)C= A+B = (a1+b1, a2+b2, c2+c2);

4)C=A-B =A +(-B);  

5)A+B=B+A;  

6)A+B+C =(A+B)+C =A+(B+C