Question

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

Answer 1

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=-\frac{9}{7} \\ \\ \end{gathered}$

Lets check:

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

$v=i+\frac{9}{7}j$

And multiplying,

$\begin{bmatrix}{1} & {} \\ {\frac{9}{7}} & {}\end{bmatrix}*\begin{bmatrix}{9} & {} \\ {-7} & {}\end{bmatrix}=1*9+\left(-7*\frac{9}{7}\right?=9+-9=0$

v and w are orthogonals.

Answer:

b=-9/7