Question
Does $\mathbf{a} \times \mathbf{b}=\mathbf{a} \times \mathbf{c}$ imply that $\mathbf{b}=\mathbf{c}$ ?
Step 1
The cross product of two vectors $\mathbf{a}$ and $\mathbf{b}$, denoted as $\mathbf{a} \times \mathbf{b}$, is a vector that is perpendicular to both $\mathbf{a}$ and $\mathbf{b}$ and thus normal to the plane containing them. Show more…
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If $\mathbf{u} \times \mathbf{v}=\mathbf{u} \times \mathbf{w}$ and $\mathbf{u} \neq \mathbf{0}$ then does $\mathbf{v}=\mathbf{w} ?$ Give reasons for your answer.
Vectors and the Geometry of Space
The Cross Product
Prove or disprove $\mathbf{a} \times(\mathbf{b} \times \mathbf{c})=(\mathbf{a} \times \mathbf{b}) \times \mathbf{c}$.
Vectors
Cross Product
Suppose that $\mathbf{a} \neq \mathbf{0}$. $$\begin{array}{l}{\text { (a) If } \mathbf{a} \cdot \mathbf{b}=\mathbf{a} \cdot \mathbf{c}, \text { does it follow that } \mathbf{b}=\mathbf{c} ?} \\ {\text { (b) If } \mathbf{a} \times \mathbf{b}=\mathbf{a} \times \mathbf{c}, \text { does it follow that } \mathbf{b}=\mathbf{c} ?} \\ {\text { (c) If } \mathbf{a} \cdot \mathbf{b}=\mathbf{a} \cdot \mathbf{c} \text { and } \mathbf{a} \times \mathbf{b}=\mathbf{a} \times \mathbf{c}, \text { does it follow }} \\ {\text { that } \mathbf{b}=\mathbf{c} ?}\end{array}$$
VECTORS AND THE GEOMETRY OF SPACE
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