27.7. Projection of Vectors

Try these first

1. 1.

   State the formula for the projection of vector u onto vector v.

   Hint

   Think about how we express one vector in the direction of another.

2. 2.

   What does the inner product ⟨u, v⟩ represent?

   Hint

   It's related to the angle between the vectors.

3. 3.

   What is the formula for projecting vector u onto vector v?

   • proj_v(u) = (⟨u
   • v⟩ / ⟨u
   • u⟩) u
   • proj_v(u) = (⟨u
   • v⟩ / ⟨v
   • v⟩) v
   • proj_u(v) = (⟨v
   • u⟩ / ⟨u
   • u⟩) u

   Hint

   Remember the correct order of vectors in the projection formula.

4. 4.

   True or False: The projection of a vector can exceed the original vector's magnitude.

   • True
   • False

   Hint

   Consider what projection represents in terms of direction.

5. 5.

   Given vectors u = (2, 3) and v = (1, 4), determine the projection of u onto v and the significance of this projection.

   Hint

   First compute the inner products.

6. 6.

   In a physical context, how can the projection of force onto a support beam help to determine safety evaluations?

   Hint

   Think about how forces interact with structural designs.