Question

Looking to receive assistance on the following problem, thank you!

Answer 1

Given:

`\begin{gathered} v=3i-4j \\ u=-2i-7i \\ w=5j \end{gathered}`

So the value is:

(a)

`\begin{gathered} u=-2i-7j \\ 2u=2(-2i-7j) \\ 2u=-4i-14j \end{gathered}`
`\begin{gathered} 2u-v=-4i-14j-(3i-4j) \\ =-4i-14j-3i+4j \\ =-7i-10j \end{gathered}`

(b)

`\begin{gathered} w=5j \\ 3w=3*5j \\ 3w=15j \end{gathered}`
`\begin{gathered} u=-2i-7i \\ 4u=4(-2i-7j) \\ 4u=-8i-28j \end{gathered}`
`\begin{gathered} 3w+4u=15j+(-8i-28j) \\ =15j-8i-28j \\ =-8i-13j \end{gathered}`

(c)

The dot product of v and u.

`\begin{gathered} v=3i-4j \\ u=-2i-7i \end{gathered}`

dot product is:

`\begin{gathered} vu=(3i-4j)\cdot(-2i-7j) \\ =-6(i\cdot i)-21(i\cdot j)+8(j\cdot i)+28(j\cdot j) \end{gathered}`

The doat product (i.i = 1) and ( j.j=1) and ( i.j=0) and ( j.i = 0)

`\begin{gathered} =-6(1)-21(0)+8(0)+28(1) \\ =-6+28 \\ =22 \end{gathered}`