Question

Vector a has magnitude 12.0 m, and vector b has magnitude 16.0 m. the scalar product vec a.b is 112 m² what is the magnitude of the vector product between these two vectors?

Answer 1

The magnitude of the vector product can be found using the equation |a x b| = |a| * |b| * sin(theta), where theta is the angle between the vectors.

Step-by-step explanation:

The magnitude of the vector product between vector a and vector b can be found using the equation:

|a x b| = |a| * |b| * sin(theta)

where |a| is the magnitude of vector a, |b| is the magnitude of vector b, and theta is the angle between vectors a and b.

In this case, the scalar product a.b is given as 112 m². The scalar product can also be expressed as |a| * |b| * cos(theta).

Since we know the magnitude of vector a is 12.0 m, the magnitude of vector b is 16.0 m, and the scalar product of a.b is 112 m², we can solve for the angle theta using the equation cos(theta) = a.b / (|a| * |b|).

Once we find theta, we can use the equation above to find the magnitude of the vector product.