Please help me with this question!!

Question

If vector C= vector a+ vector b and vector A= xi+6j, vector B=2i-3j, vector C=4j+yj, values of x and y? (i hat and j hat)

Answer 1

When vectors are in component form we can add them by adding their i and j components

So for example if A=2i+3j and B=4i-2j then their sum is (2+4)i + (3-2)j = 6i + 1j

So here A = xi + 6j

and B = 2i - 3j

So their sum is (x+2)i + (6 - 3)j

(x+2)i + 3j

But we know the sum is C = 4i + yj (you had typed 4j but i assume this is a typo)

If two vectors are equal then their components are equal

So (x+2)i = 4i

or x+2 = 4

So x = 2

and

3j = yj

So y = 3