# What is the magnitude of the cross product \(\vec{a}\) × \(\vec{b}\)?

The cross product of two vectors signifies the area swept by the two vectors at a certain angle, in form of a parallelogram.

## Answer: The value of the cross product of vectors a and b can be given as |a| |b| sinA, where A is the angle between the two vectors.

Go through the examples to understand the formula better.

**Explanation:**

Physical significance of the cross product of \(\vec{a}\) × \(\vec{b}\):

1) The magnitude of a cross product is the area of the parallelogram that they determine.

2) The direction of the cross product is orthogonal (perpendicular) to the plane determined by the two vectors.

Formulation of \(\vec{a}\) × \(\vec{b}\)

\(\vec{a}\) × \(\vec{b}\) = |a| |b| sinA (A is the angle formed between the vectors a and b)

Look at two examples shown in the figure below.

a) \(\vec{a}\) × \(\vec{b}\) = |a||b|sinA = 6 × 4 × sin 45º = 12√2

b) \(\vec{a}\) × \(\vec{b}\) = |a||b|sinA = 6 × 4 × sin 180º = -24