1. A vector and its representation

Try these first

1. 1.

   Define a vector in your own words.

   Hint

   Think about what makes a vector unique compared to other mathematical entities.

2. 2.

   How do you represent a vector graphically?

   Hint

   Remember the visual representation of arrows for vectors.

3. 3.

   What defines a vector?

   • Only magnitude
   • Only direction
   • Magnitude and direction

   Hint

   Think about what makes vectors different from scalars.

4. 4.

   Does changing the coordinate system change the vector itself?

   • True
   • False

   Hint

   Consider whether the essence of an object changes when viewed differently.

5. 5.

   Two vectors $\vec{a} = [3, 4]$ and $\vec{b} = [1, 2]$ are given. Calculate the dot product and the angle between them.

   Hint

   Use the magnitudes of both vectors and the dot product to find the angle.

6. 6.

   A vector $\vec{c}$ lies in the xy-plane and makes a 45-degree angle with the x-axis. If its magnitude is 10, represent $\vec{c}$ in component form.

   Hint

   Use trigonometric functions to resolve the vector into its components.