Vector Multiplication

Problems

practice

1. Write something.
2. Write something.
3. Derive the law of cosines from the dot product.
4. Test the cross product for associativity by determining if this equation is true.

   (A × B) × C ≟ A × (B × C)

numerical

1. Two related questions.
   1. What is the angle between two vectors if their magnitudes are 3 and 4 and their cross product is 5?
   2. What unit does this cross product have if each vector was expressed in meters?
2. Two related questions.
   1. What is the angle between two sides of a triangle if the lengths of the sides are 3 m and 4 m and the area of the triangle is 5 m²?
   2. What is the length of the remaining side?

algebraic

1. Test the scalar-vector product for distributivity by determining if this equation is true.

   (a + b)C ≟ (aC) + (bC)

2. Test the scalar-vector product for associativity by determining if this equation is true.

   a(bC) ≟ (ab)C

3. Test the dot product for distributivity over addition by determining if this equation is true.

   A ⋅ (B + C) ≟ (A ⋅ B) + (A ⋅ C)

4. Test the cross product for distributivity over addition by determining if this equation is true.

   A × (B + C) ≟ (A × B) + (A × C)