Question

Given: U= <-4, -1>, v= <0, -3>, w = <1, -1>, and z=<4, 2>.Based on the components of the given vectors, match the magnitude of each vector subtraction with its resulting value.

Answer 1

u - z is given by:

`\begin{gathered} \vec{u}-\vec{z}=\langle-4,-1\rang-\langle4,2\rang \\ =\langle-4-4,-1-2\rang=\langle-4,-3\rang \\ =\langle-8,-3\rang \end{gathered}`

Therefore, the value of ||u - z|| is given by:

`√((-8)^2+(-3)^2)=√(64+9)=√(73)\approx8.54`

Therefore, the value of ||u - z|| is approximately 8.54.

Similarly, the value of ||v - w|| is approximately 2.24.

The value of ||w - u|| is 5.

The value of ||-u - w|| is approximately 3.61.