Question

Define dot product with one example

Answer 1

Answer:

the dot product is the sum of the products of the corresponding entries of the two sequences of numbers

example

Calculate the dot product of a=(1,2,3) and b=(4,−5,6). Do the vectors form an acute angle, right angle, or obtuse angle?

Solution: Using the component formula for the dot product of three-dimensional vectors,

a⋅b=a1b1+a2b2+a3b3,

we calculate the dot product to be

a⋅b=1(4)+2(−5)+3(6)=4−10+18=12.

Since a⋅b is positive, we can infer from the geometric definition, that the vectors form an acute angle.

Answer 2

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=] The dot product, also called the scalar product, of two vector s is a number ( scalar quantity) obtained by performing a specific operation on the vector components. The dot product has meaning only for pairs of vectors having the same number of dimensions. The symbol for dot product is a heavy dot (.)