Question

Q.21 Define scalar product (Dot product) and give it's cha the two vectors. In the form of their components. Find tha scalarproduct of the two vectors. in the form of their components.
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Answer 1

Answer:

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Explanation:

The scalar or dot product of two non-zero vectors \( \vec{a} \) and \( \vec{b} \), denoted by \( \vec{a} \).\( \vec{b} \) is

\( \vec{a} \).\( \vec{b} \) = |\( \vec{a} \)| |\( \vec{b} \)| \( \cos \theta \)

where \( \theta \) is the angle between \( \vec{a} \) and \( \vec{b} \) and 0 ≤ \( \theta \) ≤ \( \pi \) as shown in the figure below.

dot product

It is important to note that if either \( \vec{a} \) = \( \vec{0} \) or \( \vec{b} \) = \( \vec{0} \), then \( \theta \) is not defined, and in this case

\( \vec{a} \).\( \vec{b} \) = 0