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what is scalar product

what is scalar product

Grade:12

2 Answers

ruchi yadav
askIITians Faculty 27 Points
7 years ago

The dot product or scalar product of two

vectorsa= [a1,a2, ...,an]andb= [b1,b2, ...,bn]is defined as:

\mathbf{a}\cdot \mathbf{b} = \sum_{i=1}^n a_ib_i = a_1b_1 + a_2b_2 + \cdots + a_nb_n

where S denotessummation notationandnis the dimension of the vector space. For instance, inthree-dimensional space, the dot product of vectors[1, 3, -5]and[4, -2, -1]is:


\begin{align}
\ [1, 3, -5] \cdot [4, -2, -1] &= (1)(4) + (3)(-2) + (-5)(-1) \\
&= 4 - 6 + 5 \\
&= 3.
\end{align}


Thank You
Ruchi
Askiitians Faculty
Indu
47 Points
7 years ago
The numerical product of the lengths of two vectors and the cosine of the angle between them.

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