Question

What is the vector sum of 7, 5 and 13, −5?

Answer 1

⇒Here, point , (7,5) and (13, -5) are points in two dimensional vector plane.

⇒Points in two dimensional system is same as representation of point in vector plane,where, x y plane is represented as i j , plane.

Point , (7,5) when written in vector form = 7 i + 5 j

Point , (13,-5) when written in vector form = 13 i - 5 j

⇒Addition of two vectors is same as Addition of two numbers, that is i component is added with i component, and j with j component.

So, 7 i + 5 j + 13 i - 5 j

= 7 i + 13 i + 5 j - 5 j→→[Addition of vectors is commutative,which is , a + b=b +a]

= 20 i +0 j

= 20 i

Answer 2

The answer is (20,0). We can determine the  sum of two vector points by adding x1 to x2 and y1 to y2. This is like adding integers, the only difference is the answer is in vector form. In here, we have (x,y). x = 7+13 and y = 5+(-5). that is why we have the (20,0) as the answer.