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For A = 3î + ĵ - 2k̂ and B = î - 2ĵ + 4k̂, find A × B, its size, and the angle between A and B.

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

For $\vec{A} = 3\hat{i} + \hat{j} - 2\hat{k}$ and $\vec{B} = \hat{i} - 2\hat{j} + 4\hat{k}$ , find $\vec{A} \times \vec{B}$ , its size, and the angle between $\vec{A}$ and $\vec{B}$ .

Need a reminder? The key ideaShow

The vector product $\vec{A} \times \vec{B}$ has size $AB\sin\theta$ and points at right angles to both (right-hand rule). From parts: $\vec{A} \times \vec{B} = (A_yB_z - A_zB_y)\hat{i} + (A_zB_x - A_xB_z)\hat{j} + (A_xB_y - A_yB_x)\hat{k}$ .

The worked solution

Have you tried it?

Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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