Question 1

What is the dot product of two vectors?

Accepted Answer

The dot product of vectors a and b is the sum of the products of their corresponding components: a1*b1 + a2*b2 + a3*b3. It produces a single scalar and equals |a||b|cos(theta), where theta is the angle between them.

Question 2

What is the cross product?

Accepted Answer

The cross product is defined only for 3D vectors. It returns a new vector perpendicular to both inputs with magnitude |a||b|sin(theta). The direction follows the right-hand rule.

Question 3

How do you find the angle between two vectors?

Accepted Answer

Use the formula theta = arccos( (a · b) / (|a| |b|) ). First compute the dot product and both magnitudes, divide, then take the inverse cosine. The result is between 0 and 180 degrees.

Question 4

Does this calculator support 2D vectors?

Accepted Answer

Yes. Toggle between 2D and 3D mode. In 2D mode the cross product is shown as a scalar (the z-component), which is the signed area of the parallelogram formed by the two vectors.