Vector Cross Product Calculator

Effortless Calculations at Your Fingertips

Use this vector cross product calculator to find A × B fast. It works with two three dimensional vectors. You see each i j and k step. You get the magnitude of the result. A simple sketch shows A and B and A × B. Students gain more from the math with clear steps.

How to Use This Tool

Enter two vectors and press the button to compute A × B. Inputs accept integers and decimals and negative values. Blank fields count as zero.

• Vector A x means the x component of A
• Vector A y means the y component of A
• Vector A z means the z component of A
• Vector B x means the x component of B
• Vector B y means the y component of B
• Vector B z means the z component of B

The calculator follows the standard cross product formula. i component equals Ay times Bz minus Az times By. j component equals Az times Bx minus Ax times Bz. k component equals Ax times By minus Ay times Bx. The result vector stands perpendicular to both inputs. Direction follows the right hand rule.

Step-by-Step Instructions

1. Type the x y and z values for Vector A
2. Type the x y and z values for Vector B
3. Press Calculate A × B
4. Read the step section for i j and k
5. Check the Result line for the vector and magnitude
6. View the sketch for A and B and A × B

Why Choose This Calculator?

You get a clear breakdown for each component and the final length. Numbers display as integers or round to four decimals. The sketch helps you see direction and scale at a glance. This vector cross product calculator suits study and quick checks. It helps you verify manual work without strain.

A Quick Look at Vectors

The cross product builds a new vector from two inputs. That new vector stands perpendicular to A and B. Its length equals the area of the spanned parallelogram. Units follow the product of the input units. Here is how to read the output.

• A × B shows the three components of the result
• Magnitude shows the length of that result
• The sign of j follows the standard formula
• The sketch uses an isometric view to show depth

Common uses include these cases.

• Physics torque r × F for a lever arm
• Area of a parallelogram from two sides
• Surface normal for lighting in computer graphics
• Angular momentum r × p in mechanics
• Test for parallel inputs with a near zero result

Smooth and Simple Interface

Work flows in one pass from inputs to results. You enter values then you see steps and the sketch. The process stays direct and clear. Results update with each click. Use small or large values without extra setup.

A Sensory Experience

A single click gives a crisp update on screen. Numbers appear then lines draw so you focus on the math. Simple tasks feel calm when steps read clean and clear.

Final Thoughts

Keep these notes in mind for best results.

• This tool works with three dimensional vectors only
• Empty inputs count as zero values
• Direction follows the right hand rule
• Zero vectors skip drawing in the sketch
• Non integer values round to four decimal places
• Very large values may scale down in the sketch

Try the vector cross product calculator on a few pairs. Check the steps then compare with hand work to build trust. Fast math with clear checks and solid learning.