Any vector `x` in `R^3` can be written as `x=x_1i+x_2j+x_3k`
where `i,j,k` are unit vectors along the three directions.
Now given matrix is `A=[[a,b],[c,d]]` . According to the problem the vector `v` is the column vector of the matrix `A` .
So we can take `v=[[a],[c]]` which can be wriiten as `v=ai+cj+0k` , a vector in `R^3.`
`=cx_3i-ax_3j+(ax_2-cx_1)k` . Answer.
Any vector in `R^3 ` can be written as (x,y,z).
So vector v=(a,c,0) and w=(b,d,0) are in `R^3`
`vx w =[[i,j,k],[a,c,0],[b,d,0]]`
`hati,hatj, and hatk` are mutually perpendicular directions.