Answer :

To find the dot product of the vectors [tex]\( F = 2i + 4j \)[/tex] and [tex]\( S = i + 5j \)[/tex], we can use the formula for the dot product of two vectors:

[tex]\[ F \cdot S = (F_i \cdot S_i) + (F_j \cdot S_j) \][/tex]

Here's a step-by-step calculation:

1. Identify the components of each vector:
- The vector [tex]\( F \)[/tex] has components [tex]\( F_i = 2 \)[/tex] and [tex]\( F_j = 4 \)[/tex].
- The vector [tex]\( S \)[/tex] has components [tex]\( S_i = 1 \)[/tex] and [tex]\( S_j = 5 \)[/tex].

2. Multiply the corresponding components:
- Multiply the [tex]\( i \)[/tex]-components: [tex]\( F_i \cdot S_i = 2 \cdot 1 = 2 \)[/tex].
- Multiply the [tex]\( j \)[/tex]-components: [tex]\( F_j \cdot S_j = 4 \cdot 5 = 20 \)[/tex].

3. Add the products obtained in step 2:
- [tex]\( F \cdot S = 2 + 20 = 22 \)[/tex].

Therefore, the dot product of vectors [tex]\( F \)[/tex] and [tex]\( S \)[/tex] is 22.

This matches option D, but with no unit associated (e.g., J for Joules), the numerical answer is simply 22.

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Rewritten by : Barada