I really need some assistance with the following problem:
"Find all unit vectors in the plane determined by u = (3,0,1) and v = (1,-1,1) that are perpendicular to the vector w = (1,2,0)".
The problem for me is that I donīt really know how to approach planes in general. For example, how do I calculate what plane is determined by the two vectors u and v?
What would u and v look like if they were serparate planes?
If someone know a website that explains the basics of vector planes I would appreciate the adress.
Thanks in advance
In the same way, any vector of the form will lie in the plane defined by and . We may think of the grid of unit squares defined by and as having been replaced by a grid of parallelograms defined by and .
So if and , any vector lying in the plane determined by and will be of the form .
Now two vectors are perpendicular if their dot (scalar) product is zero. So this vector is perpendicular to , if:So the vector will be of the form
All that remains is to find unit vectors in this form. So that will be whereSo I reckon there's our answer: the unit vectors are