Vector Product of Two Vectors

The vector product is also known as the cross product of two vectors. This results in a new vector. For all Class 11 students in Physics, one key concept of the cross product is that this resultant vector is perpendicular to the plane containing the original two vectors. The magnitude of this new vector is calculated by multiplying the magnitudes of the two initial vectors and the sine of the angle between them. The direction of the resulting vector is determined by the right-hand rule.

The product of two equal vectors depends on what type of multiplication we are using. 

1. Dot Product: The dot product of two equal vectors is the square of the magnitude of the vector. This is because the angle between two equal vectors is 0°, and the cosine of 0° is 1.

2. Cross Product: The vector product or cross product of two equal vectors is a zero vector (or null vector). This is because the angle between the vectors is zero, and the sine of 0° is 0.

The dot product of a vector with itself is the magnitude's square. When we multiply a vector by itself using the dot product, the angle between them is always zero. That's because the cosine of a 0° angle is 1. The dot product simplifies to the product of the magnitudes of the two vectors. And, in this case, it is the magnitude of the vector that is multiplied by itself. This operation results in a scalar quantity.