- Math colloquium
- “Learning Mathematics in a Language Not Your Own”
- Dr. Kyriakos Petakos
- Wednesday, Sept. 16, 2:45
- Newton 204
- Extra credit (up to 2 points of homework credit) for attending and writing ca. 1 paragraph re what struck you as interesting/important and why
- Section 12.3
- Produces scalar result
- Dot product =
- u1v1 + u2v2 + u3v3
- Or cos(a) |u| |v|
- Find angle between vectors: cos-1( (u1v1 + u2v2 + u3v3) / |u||v| )
- Look at proof that dot product gives angle between vectors
- Projections?
- Examples
- What is the projection of ⟨1,1,3⟩ onto ⟨2,1,0⟩?
What is its scalar component in the direction of ⟨2,1,0⟩?
- What is the angle between ⟨3,0,2,4,1⟩ and ⟨0,0,3,5,0⟩?
- cos a = ⟨3,0,2,4,1⟩⋅⟨0,0,3,5,0⟩ / |⟨3,0,2,4,1⟩||⟨0,0,3,5,0⟩|
- = 26 / (√30 √34)
- = cos( 0.81 )
- a = 0.61 radians
- What is the projection of ⟨1,1,3⟩ onto ⟨2,1,0⟩?
What is its scalar component in the direction of ⟨2,1,0⟩?
- The cross product
- Read section 12.4