Question

if w = <3.5, -6> and z = <-1.5, -4>, what is the resulting vector for 2w - z?
a. <5, -2>
b. <10, -4>
c. <8.5, -8>
d. <5.5, 12>

Explanation:

Step1: Calculate \(2\mathbf{w}\)

To find \(2\mathbf{w}\), we multiply each component of \(\mathbf{w}=\langle 3.5, -6
angle\) by 2.
For the \(x\)-component: \(2\times3.5 = 7\)
For the \(y\)-component: \(2\times(-6)=-12\)
So, \(2\mathbf{w}=\langle 7, -12
angle\)

Step2: Subtract \(\mathbf{z}\) from \(2\mathbf{w}\)

Given \(\mathbf{z}=\langle -1.5, -4
angle\), we subtract \(\mathbf{z}\) from \(2\mathbf{w}\) by subtracting the corresponding components.
For the \(x\)-component: \(7-(-1.5)=7 + 1.5=8.5\)
For the \(y\)-component: \(-12-(-4)=-12 + 4=-8\)
So, \(2\mathbf{w}-\mathbf{z}=\langle 8.5, -8
angle\)

Answer:

C. \(\langle 8.5, -8
angle\)