Dot Product Calculator
- Enter two or more vectors and click Calculate to find the dot product.
- Define each vector with parentheses "( )", square brackets "[ ]", greater than/less than signs "< >", or a new line.
- Separate terms in each vector with a comma ",". The number of terms must be equal for all vectors.
- Vectors may contain integers and decimals, but not fractions, functions, or variables.
About Dot Products
In linear algebra, a dot product is the result of multiplying the 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 adding them together, or (a1 * b1) + (a2 * b2) + (a3 * b3) .... + (an * bn). We can calculate the dot product for any number of vectors, however all vectors must contain an equal number of terms.
Find a ⋅ b when a = <3, 5, 8> and b = <2, 7, 1>
a ⋅ b = (a1 * b1) + (a2 * b2) + (a3 * b3)
a ⋅ b = (3 * 2) + (5 * 7) + (8 * 1)
a ⋅ b = 6 + 35 + 8
a ⋅ b = 49
- Khan, Salman "Vector dot product and vector length", The Khan Academy, Vector Dot Product and Vector Length.