In a given linear algebra, a dot product is the result of multiplying individual numerical values in two or more vectors. If we defined vector ‘A’ as <a1, a2, a3…. an> and vector ‘B’ as <b1, b2, b3… bn> we can find the dot product by multiplying the corresponding values in each vector and then adding them up together.
This gives us the formula which is- (a1 * b1) + (a2 * b2) + (a3 * b3) …. + (an * bn). We can calculate the dot product for any number of vectors; however, all the vectors must contain an equal number of terms (say 3 in A and 3 in B). For this we need to follow these steps:
Enter two or more vectors and click the ‘Calculate’ button to find the dot product.
Define each vector with brackets “( )”, square brackets “[ ]”, greater than/less than signs “< >”, or a new line.
Separate terms in each vector with a comma “,” containing integers and decimals but not fractions, functions, or variables.
Find a ⋅ b when a = <3, 5, 8> and b = <2, 7, 1>
Gives us: a ⋅ b = (3 * 2) + (5 * 7) + (8 * 1) implies a ⋅ b = 49