Are ( -1.5, 6)^{T} and (2, 2)^{T} orthogonal?

No: the dot product is -3 + 12 = 9.

The dot product is not zero, so the two vectors are not orthogonal. You don't even have to think about lengths. (Remember that this test detects orthogonality no matter what the length of the vectors). The next chapter will discuss what a non-zero dot product of two vectors gives you.

You have reached the end of the chapter. Normally at this point you would review the following terms:

- Length of a vector as a dot product.
- Some facts about the dot product and vector length.
- Unit vector (review.)
- Easy way to get confused.
- Unit vector used to express direction.
- Dot product of orthogonal vectors.
- Way to construct a 2D vector orthogonal to another one.
- Unit Normal.
- Unit normal in 3D.
- Definition of the slope of a 2D line (review.)
- Relationship between slopes of perpendicular 2D lines.

Click on a term to see where it was discussed in this chapter. Remember to click on the "Back" arrow of your browser to get back to this page.

You have reached the end of the chapter.