Math
Vector dot product
Compute the scalar dot product of two three-dimensional vectors.
Calculators / Math / Vector projection
Vector projection calculator
Project vector A onto the direction of vector B.
On this page
Projection x1.66
Projection y2.08
Projection z2.49
Calculator controls
How to calculate
Project vector A onto the direction of vector B.
Projection x = (ax*bx+ay*by+az*bz)/(bx^2+by^2+bz^2)*bx; Projection y = (ax*bx+ay*by+az*bz)/(bx^2+by^2+bz^2)*by; Projection z = (ax*bx+ay*by+az*bz)/(bx^2+by^2+bz^2)*bz
Worked example
Vector A x: 1; Vector A y: 2; Vector A z: 3; Vector B x: 4; Vector B y: 5; Vector B z: 6.
Projection x: 1.66 ; Projection y: 2.08 ; Projection z: 2.49 .
Assumptions and limits
Vector B must be nonzero. The result is a vector parallel to B, not its perpendicular component.
Results are rounded for display; calculations use unrounded values. Read our calculation methodology.
Understanding the result
Project vector A onto the direction of vector B.
When this tool is useful
Projection x = (ax*bx+ay*by+az*bz)/(bx^2+by^2+bz^2)*bx; Projection y = (ax*bx+ay*by+az*bz)/(bx^2+by^2+bz^2)*by; Projection z = (ax*bx+ay*by+az*bz)/(bx^2+by^2+bz^2)*bz
Understanding your inputs
| Input | What to enter |
|---|---|
| Vector A x | Enter a number of at least -1000000000000 and no more than 1000000000000. |
| Vector A y | Enter a number of at least -1000000000000 and no more than 1000000000000. |
| Vector A z | Enter a number of at least -1000000000000 and no more than 1000000000000. |
| Vector B x | Enter a number of at least -1000000000000 and no more than 1000000000000. |
| Vector B y | Enter a number of at least -1000000000000 and no more than 1000000000000. |
| Vector B z | Enter a number of at least -1000000000000 and no more than 1000000000000. |
Frequently asked questions
What assumptions does this calculation use?
Vector B must be nonzero. The result is a vector parallel to B, not its perpendicular component.
How is the result calculated?
Projection x = (ax*bx+ay*by+az*bz)/(bx^2+by^2+bz^2)*bx; Projection y = (ax*bx+ay*by+az*bz)/(bx^2+by^2+bz^2)*by; Projection z = (ax*bx+ay*by+az*bz)/(bx^2+by^2+bz^2)*bz