21.9.1. Orthogonal Vectors

Try these first

1. 1.

   What are orthogonal vectors?

   Hint

   Think about the angles formed between the vectors.

2. 2.

   Define an orthonormal set.

   Hint

   What additional condition must be met besides being orthogonal?

3. 3.

   What is the dot product of two orthogonal vectors?

   • 1
   • 0
   • Unknown

   Hint

   What does their angle look like?

4. 4.

   Is an orthonormal set always composed of orthogonal vectors?

   • True
   • False

   Hint

   Consider both properties that define orthonormality.

5. 5.

   Given vectors v1 = (2, 3, 4) and v2 = (1, 2, -3), use the Gram-Schmidt process to create an orthonormal set.

   Hint

   Follow the steps of normalization and projection carefully.

6. 6.

   Prove that the vectors (1, 1) and (-1, 1) are orthogonal by calculating their dot product.

   Hint

   Remember the formula for dot product calculation.