Find two linearly independent vectors perpendicular to vector v

Question

Find two linearly independent vectors perpendicular to the vector v=[-2,3,-5]

Answer 1

You should use the lesson notes that you were given to find a vector that is perp to this one. One way is to take the cross product v with any of the axes vectors i, j, or k. The result will be perp because it is a cross product. Then, to get the other perp vector, use the cross product again. - Ben

Answer 2

Two vectors are perpendicular if their dot product is zero, and given a fixed vector in three-dimensional space, there are an infinite number of vectors perpendicular to it.

 

For example, <3,2,0> is perpendicular to v because <3,2,0><-2,3,-5>=0.

Another example would be <0,5,3>. These two vectors are also linearly independent.