If vector a has a magnitude of 1/√3 and vector b has a magnitude of 4, what is the value of a × b if the angle between them is 60°?

To find the magnitude of the cross product of two vectors ( a ) and ( b ), we can use the formula:

[

|a \times b| = |a| \cdot |b| \cdot \sin(\theta)

]

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

In this case, the magnitudes are given as:

• ( |a| = \frac{1}{\sqrt{3}} )

• ( |b| = 4 )

The angle ( \theta ) is ( 60^\circ ). We know that ( \sin(60^\circ) = \frac{\sqrt{3}}{2} ).

Substituting these values into the formula:

[

|a \times b| = \left(\frac{1}{\sqrt{3}}\right) \cdot 4 \cdot \sin(60^\circ)

]

[

= \left(\frac{1}{\sqrt{3}}\right) \cdot 4 \cd