Calculate Product of Three Dimensional Vectors
Calculate the product of three dimensional vectors(3D Vectors) for entered vector coordinates.
Calculator
Formula
The 3D vectors are using the x-y-z axes.- α is the angle between u and the x-axis.
- β is the angle between u and the y-axis.
- γ is the angle between u and the z-axis.
Therefore scalar product for unit vector:
- u1 = u ⋅ i = 1 × 1 × cos α = cos α
- u2 = u⋅ j = 1 × 1 × cos β = cos β
- u3 = u ⋅ k = 1 × 1 × cos γ = cos γ
the unit vector u can be written as:
u = cos α i + cos β j + cos γ k
Example
Find the dot product of vectors: A = (2, 3, 4) B = (1, 5, 2)
Dot Product = (2×1) + (3×5) + (4×2)
= 2 + 15 + 8 = 25
Frequently Asked Questions
What is a dot product?
The dot product is the multiplication of corresponding vector components followed by addition.
What is another name for dot product?
The dot product is also called the scalar product.
What does a zero dot product mean?
It means the vectors are perpendicular.
