IB Mathematics Analysis and Approaches Question Type 5: Finding Distance Between Any Two Simple Vectors Exercises

Express the distance between the points $(a,b)$ and $(b,a)$ in terms of $a$ and $b$.

Calculate the distance between $(3,7,-2)$ and $(-1,-3,4)$.

Find the distance between the points $(2\cos \theta ,2\sin \theta )$ and $(2,0)$.

Show that the distance from the origin to the point $(x,y,z)$ is $\sqrt{x^2+y^2+z^2}$.

Find the distance between the points $(1,0,2)$ and $(0,1,2)$.

Calculate the distance between the points $(-1,2,-3)$ and $(4,-2,1)$.

Determine the distance between the points $(2,-3)$ and $(-4,5)$.

Find the distance between the points $\,(0,0)\,$ and $\,(5,12)\,$ in the plane.

Express the distance between $(5,5)$ and $(t,t^2)$ as a function of $t$.

Calculate the distance between the points $(1,1,4)$ and $(4,3,2)$.

Find the distance between $\left(\frac{1}{2},-\frac{1}{3}\right)$ and $\left(\frac{2}{3},\frac{3}{4}\right)$ in the plane.

Compute the distance between the vectors $(-2,3,1)$ and $(4,-1,5)$.