2.1. Dot Product

Try these first

1. 1.

   Calculate the dot product for vectors a = (1, 2) and b = (3, 4).

   Hint

   Use the formula a · b = a1 * b1 + a2 * b2.

2. 2.

   What is the dot product of a vector with itself, for example, c = (5, 5)?

   Hint

   Remember, the dot product of a vector with itself yields the square of its magnitude.

3. 3.

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

   • 1
   • 0
   • -1

   Hint

   Remember the geometric interpretation.

4. 4.

   True or False: The dot product yields a vector result.

   • True
   • False

   Hint

   Think about the nature of the output.

5. 5.

   Given three vectors: a = (3, 1, 2), b = (1, 4, 0), and c = (2, -1, 3), find the dot product of a and b, and then determine the angle between c and the resultant vector of a and b.

   Hint

   Don't forget to calculate the magnitudes for the final angle determination.

6. 6.

   Two vectors have a dot product of -12, Suggest possible values for their magnitudes and the angle between them.

   Hint

   Think about how multiplying positive and negative components give a negative value?