2. Mathematical operations with vectors

Try these first

1. 1.

   Calculate the dot product of vectors a = [1, 2, 3] and b = [4, 5, 6].

   Hint

   Multiply corresponding components and add them.

2. 2.

   What is the cross product of vectors a = [1, 0, 0] and b = [0, 1, 0]?

   Hint

   Think of the right-hand rule for direction.

3. 3.

   What is the result of the dot product of two vectors?

   • A vector
   • A scalar
   • A matrix

   Hint

   Remember to consider the properties of scalar vs. vector.

4. 4.

   True or False: The cross product of two vectors is always orthogonal to the plane containing them.

   • True
   • False

   Hint

   Think of how vectors interact in three-dimensional space.

5. 5.

   Given vectors a = [3, 4] and b = [4, -3], calculate their dot product and interpret the result geometrically.

   Hint

   Visualize the vectors on a graph.

6. 6.

   Using a = [1, 2, 3] and b = [4, 5, 6], compute the tensor product and describe its significance.

   Hint

   Focus on how each element in the result relates to each combination of inputs.