To multiply or divide a vector by a scalar in this tuple notation, you distribute the scalar over the tuple, multiplying or dividing both components: $$3(1,2)=(3,6)\qquad (3,6)\div3=(1,2)$$

To add two vectors together in this notation, you add the \(x\) values and the \(y\) values separately: $$(3,2)+(-1,1)=(3-1 ,2+1) = (2,3)$$

The magnitude of a vector \((x,y)\) is $$\abs{(x,y)} = \sqrt{x^2+y^2}$$ For example, the magnitude of the vector (2,3) above is $$\abs{(2,3)} = \sqrt{2^2+3^2} = \sqrt{4+9} = \sqrt{13} \approx 3.6$$