Find the distance between the two vectors.
-$$\mathbf { u } = ( 6 , - 12 ) , \mathbf { v } = ( - 12,12 )$$
A) 30
B) 150
C) 6
D) 900

Question

Quizplus · Accepted Answer

The distance between two vectors $\mathbf{u} = (u_1, u_2)$ and $\mathbf{v} = (v_1, v_2)$ in a 2-dimensional space is given by the formula $\sqrt{(v_1 - u_1)^2 + (v_2 - u_2)^2}$. Substituting the given values, we get $\sqrt{(-12 - 6)^2 + (12 - (-12))^2} = \sqrt{(-18)^2 + 24^2} = \sqrt{324 + 576} = \sqrt{900} = 30$.

Find the Distance Between the Two Vectors u=(6,−12),v=(−12,12)\mathbf { u } = ( 6 , - 12 ) , \mathbf { v } = ( - 12,12 )u=(6,−12),v=(−12,12)

Find the Distance Between the Two Vectors $\mathbf { u } = ( 6 , - 12 ) , \mathbf { v } = ( - 12,12 )$