Chapter 11.3, Problem 4E

(a)

To determine

To calculate: The dot product of two different vector $\left(u·v\right)$ where vectors, $u=\langle 4,10\rangle$ and $v=\langle -2,3\rangle$.

(b)

To determine

To calculate: The dot product of two same vector $\left(u·u\right)$ where vectors, $u=\langle 4,10\rangle$ and $v=\langle -2,3\rangle$.

(c)

To determine

To calculate: The square of magnitude ${\Vert v\Vert }^2$ where vectors, $u=\langle 4,10\rangle$ and $v=\langle -2,3\rangle$.

(d)

To determine

To calculate: The dot product of the vector $\left(u·v\right)v$ where vectors, $u=\langle 4,10\rangle$ and $v=\langle -2,3\rangle$.

(e)

To determine

To calculate: The dot product of the vector $u·\left(3v\right)$ where vectors, $u=\langle 4,10\rangle$ and $v=\langle -2,3\rangle$.