Question

Find b so that the vectors v=i−bj and w=9i−7j are orthogonal.

Answer 1

Step-by-step explanation:

For those vectors to be orthogonal, v*w=0.

In this case:

`\begin{bmatrix}{1} & {} \\ -{b} & {}\end{bmatrix}*\begin{bmatrix}{9} & {} \\ -{7} & {}\end{bmatrix}=1*9+-b*-7=0`
`\begin{gathered} 9+7b=0 \\ 7b=-9 \\ b=-(9)/(7) \\ \\ \end{gathered}`

Lets check:

If b=-9/7, then v=i-(-9/7)j, and we have:

`v=i+(9)/(7)j`

And multiplying,

`\begin{bmatrix}{1} & {} \\ {(9)/(7)} & {}\end{bmatrix}*\begin{bmatrix}{9} & {} \\ {-7} & {}\end{bmatrix}=1*9+\left(-7*(9)/(7)\right?=9+-9=0`

v and w are orthogonals.

Answer:

b=-9/7