Help me with vectors?

Consider the displacement vectors with m=meters


A= (3i-3j)m


B=(i-4j)m


C=(-2i+5j)m





Find D=A+B+C and E=-A-B+C





Please explain your steps

Help me with vectors?
just add up the components





x component of A+B+C = 3 + 1 - 2 = 2


so you have 2i in the answer.


Do the same for j and k components.





in the second problem, you have -A-B+C


so it's -(3) - (1) + (-2) = -6 for the i component


do likewise for the other components





Have fun.
Reply:These coordinates you have are in rectangular format, that is in displacements in the east/west direction, and the north/south direction. ( there are other ways of describing this, but this will work for now ).





(3i-3j) would indicate going 3m west and 3m south, or -3m north.





When you add the three vectors you get the following:


(3i-3j) + (i-4j) + (-2i+5j) which translates to


(3i+i-2i-3j-4j+5j) which translates to


(2i-2j)





Subtracting one of the vectors is the same as addition, but both the i and j terms are negated. thus we get


(3i-3j) - (i-4j) + (-2i+5j) which translates to


(3i-i-2i-3j+4j+5j) which translates to


(0i+6j)
Reply:Just substitute the subject into the main equatio:D=A+B+C


D=A+B+C


=(3i-3j)m+(i-4j)m+(-2i+5j)m


=[3i+i-2i-3j-4j+5j]m


=(2i-2j)m


=2(i-j)m





E=-A-B+C


=-(3i-3j)m-(i-4j)m+(-2i+5j)m


=[-3i-i-2i+3j+4j+5j]m


=(-6i+12j)m


=6(2j-i)m