Hi! I am currently working on some calc2 online homework problems concerning the cross product. I understand how the cross product works, but I am not sure how to apply it to this question. I know that my values for the i and k components of the vector are correct, but I am not sure how to go about finding the correct j component vector value. If someone can help me answer this problem I would really appreciate it.
A useful formula you should know (and prove) is the following:
If you are given two vectors, A and B, then:
$$\mathbf{A} \times \mathbf{B} = \Vert \mathbf{A} \Vert \cdot \Vert \mathbf{B} \Vert \sin(\theta)\mathbf{n}$$
Where $\mathbf{n}$ is the unit vector normal to the plan spanned by the original two vectors and $\theta$ the angle between them. In this case, we have $\mathbf{n} = \langle 0, 1, 0 \rangle$ and $\theta = \pi/3$.