8.6.2 – Orthogonal Vectors

1. 8.6.2 – Orthogonal Vectors

2. At the end of yesterday, we addressed the case of using the dot product to determine the angles between vectors • Similar to equations from algebra, we can talk about relationship of vectors as well • Parallel • Perpendicular • Neither

3. Orthogonal • Two nonzero vectors u and v are said to be orthogonal (perpendicular) if • Same as saying the angle ϴ is a right angle/90 degrees

4. When finding vectors that are orthogonal, there may be an infinite number of solutions • Easiest way; pick one number with opposite sign and assign it to the first; then, find a second number such that they will add to zero • Takes some experimentation!

5. Example. Find a vector orthogonal to the vector u = {-6, 6}.

6. Example. Find a nonzero vector orthogonal to v = 2i – 4j

7. Example. Find two nonzero vectors orthogonal to the vector u = {-10, 3}

8. P,P,N • To determine if vectors are parallel, perpendicular, or neither, we can use the dot product theorem from yesterday, and look for the following; • Parallel; if tan(ϴ) is the same for both vectors, then they are parallel • Perpendicular; dot product = 0 • Neither; none of the above

9. Example. Determine whether uand v are orthogonal, parallel, or neither. • u = {2, -3} v = {-6, 9}

10. Example. Determine whether uand v are orthogonal, parallel, or neither. • u = {7, -2} v = {-4, -14}

11. Assignment • Pg. 679 • 31-42