Question

a vector $a$ has magnitude 6 units and is in the direction of the + x-axis. vector $b$ has magnitude of 4 units and lies in the xy-plane, making an angle $30^\circ$ with the +x-axis. find the product $a \times b$
12.0 units
13.9 units
20.8 units
24.0 units
this is a required question

Explanation:

Step1: Recall cross product magnitude formula

The magnitude of the cross product of vectors $\vec{A}$ and $\vec{B}$ is given by $|\vec{A} \times \vec{B}| = |\vec{A}| |\vec{B}| \sin\theta$, where $\theta$ is the angle between the two vectors.

Step2: Identify given values

$|\vec{A}| = 6$ units, $|\vec{B}| = 4$ units, $\theta = 30^\circ$, and $\sin(30^\circ) = 0.5$.

Step3: Substitute values into formula

$$|\vec{A} \times \vec{B}| = 6 \times 4 \times \sin(30^\circ)$$
$$|\vec{A} \times \vec{B}| = 6 \times 4 \times 0.5$$

Step4: Calculate the result

$$|\vec{A} \times \vec{B}| = 12.0$$

Answer:

12.0 units