Question

given ( mathbf{u}=langle 5,6
angle ) and ( mathbf{v}=langle 4,6
angle ), find ( 10 mathbf{u}-8 mathbf{v} ).

( 10 mathbf{u}-8 mathbf{v}=langlesquare,square
angle )
(simplify your answers.)

Explanation:

Step1: Calculate \(10\mathbf{u}\)

To find \(10\mathbf{u}\) where \(\mathbf{u}=\langle5,6
angle\), we multiply each component of \(\mathbf{u}\) by 10. So, \(10\mathbf{u}=\langle10\times5, 10\times6
angle=\langle50, 60
angle\).

Step2: Calculate \(8\mathbf{v}\)

To find \(8\mathbf{v}\) where \(\mathbf{v}=\langle4,6
angle\), we multiply each component of \(\mathbf{v}\) by 8. So, \(8\mathbf{v}=\langle8\times4, 8\times6
angle=\langle32, 48
angle\).

Step3: Subtract \(8\mathbf{v}\) from \(10\mathbf{u}\)

To find \(10\mathbf{u}-8\mathbf{v}\), we subtract the corresponding components of \(8\mathbf{v}\) from \(10\mathbf{u}\). So, for the first component: \(50 - 32 = 18\), and for the second component: \(60 - 48 = 12\). Thus, \(10\mathbf{u}-8\mathbf{v}=\langle18, 12
angle\).

Answer:

\(\langle 18, 12
angle\)