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Math with Vector Notation

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: $$3(1,2)=(3,6)(3,6)÷3=(1,2)$$

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