Question

Vector A has magnitude 13.0 m and vector B has magnitude 16.0 m. The scalar product A.B is 116 m2. What is the magnitude of the vector product between these two vectors? Express your answer with appropriate units.

Answer 1

Answer:

$\text{Vector product}=172.66\ m^2$

Explanation:

Given that,

The magnitude of vector A, $|A|=13\ m$

The magnitude of vector B, $|B|=16\ m$

Scalar product of A and B, $A{\cdot} B=116\ m^2$

The formula for the scalar product is given by :

$A{\cdot} B=|A||B|\cos\theta$

Where, $\theta$ is the angle between A and B.

$\cos\theta=\dfrac{116}{13\times 16}\\\\\theta=\cos^{-1}\left(0.5576\right)\\\\\theta=56.11^{\circ}$

The formula for the vector product is given by :

$A\times B=|A||B|\sin\theta\\\\=13\times 16\times \sin56.11\\\\=172.66\ m^2$

So, the vector product between these two vectors is $172.66\ m^2$.