Calculators

Algebra

Calculator Use

• 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.... a_n> and vector b as <b₁, b₂, b₃... b_n> 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) .... + (a_n * b_n). We can calculate the dot product for any number of vectors, however all vectors must contain an equal number of terms.

Example

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

Further Reading

• Khan, Salman "Vector dot product and vector length", The Khan Academy, Vector Dot Product and Vector Length.