linear algebra – How to construct matrices whose orthogonal complement of the space of lines is covered by a vector

enter the description of the image here

This is an example of a problem, some of them rather use the Column Space Add-in. My way of thinking was that since the complement of the space of the lines is the null space of the matrix, I would create a matrix so that the matrix multiplied by the null space equals 0. What would be the right way to think for a problem like this?