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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.

  • $\begingroup$ Well, do you know what direction the second component will have? Using the right hand rule, $v \times w$ is not the same as $w \times v$. Also, how are you getting the magnitude of the cross product? Do you have a formula? $\endgroup$ – Carser May 5 '14 at 20:02

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 $\theta = \pi/3$.

  • $\begingroup$ Co since v and w are vectors of length 3, then V X W= 3*3sin(pi/3)(1) for the second coordinate and that would be equivalent to .1644842487, but it is saying that that answer is also incorrect for the second coordinate. What am I dining wrong? $\endgroup$ – user124539 May 5 '14 at 22:32
  • $\begingroup$ Your calculator is in degree mode. $\pi/3$ is an angle measured in radians. ;) $\endgroup$ – Kaj Hansen May 5 '14 at 22:40

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