Calculate The Dot Product of A= (1, 2, 3) and B= (4, −5, 6)

Calculate the dot product of a= (1, 2, 3) and b= (4, −5, 6) . What type of angle the vectors will form?

SOLUTION:

Using the formula for the dot product of three-dimensional vectors as follows,

a⋅b = a1b1+a2b2+a3b3,

We may calculate the dot product to be:

a⋅b = a1b1+a2b2+a3b3

a⋅b = 1(4)+2(-5)+3(6)

a⋅b = 4 – 10 + 18 =12

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

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