Topic explanation

Standard explanation

The multiplication of two vectors according to a defined mathematical rule is called the product of vectors.

Key points

• Explain the meaning of vector multiplication.
• Differentiate between dot product and cross product.
• A⃗ · B⃗ = AB cos θ (scalar result).
• A⃗ × B⃗ = AB sin θ n̂ (vector result).
• Dot → cosine → scalar; Cross → sine → vector.
• Perpendicular vectors have zero dot product.
• Parallel vectors have zero cross product.
• Work uses the dot product; torque uses the cross product.

Labelled diagram