Answer:
The magnitude of [tex]\vec b[/tex] is approximately 5.774.
Explanation:
According to the definition of dot product:
[tex]\vec a\bullet \vec b = \|\vec a \|\cdot \|\vec b\|\cdot \cos \theta[/tex]
Where:
[tex]\|\vec a\|[/tex], [tex]\|\vec b\|[/tex] - Norms (or magnitudes) of [tex]\vec a[/tex] and [tex]\vec b[/tex], dimensionless.
[tex]\theta[/tex] - Internal angle between [tex]\vec a[/tex] and [tex]\vec b[/tex], measured in sexagesimal degrees.
The magnitude of [tex]\vec b[/tex] is therefore cleared:
[tex]\|\vec b\| = \frac{\vec a \bullet \vec b}{\|\vec a\|\cdot \cos \theta}[/tex]
Given that [tex]\vec a \bullet \vec b = 20[/tex], [tex]\|\vec a\| = 4[/tex] and [tex]\theta = 30^{\circ}[/tex], the magnitude of [tex]\vec b[/tex] is:
[tex]\|\vec b\| = \frac{20}{4\cdot \cos 30^{\circ}}[/tex]
[tex]\|\vec b\| \approx 5.774[/tex]
The magnitude of [tex]\vec b[/tex] is approximately 5.774.
