To find the dot product of the vectors [tex]\((2, 4)\)[/tex] and [tex]\((1, -2)\)[/tex], follow these steps:
1. Identify the components of the vectors:
- The first vector is [tex]\((2, 4)\)[/tex].
- The second vector is [tex]\((1, -2)\)[/tex].
2. Multiply the corresponding components of the vectors:
- Multiply the first components: [tex]\(2 \times 1 = 2\)[/tex].
- Multiply the second components: [tex]\(4 \times -2 = -8\)[/tex].
3. Add the products obtained from the previous step:
- Sum the products: [tex]\(2 + (-8)\)[/tex].
4. Calculate the result:
- [tex]\(2 - 8 = -6\)[/tex].
Hence, the dot product of the vectors [tex]\((2, 4)\)[/tex] and [tex]\((1, -2)\)[/tex] is [tex]\(-6\)[/tex].
