Question Type 2: Finding the cross product using different operations of vectors Exercises

Let $\mathbf{a}=(1,0,1)$, $\mathbf{b}=(3,2,1)$, and $\mathbf{c}=(5,6,1)$. Compute $(\mathbf{a}+\mathbf{b})\times \mathbf{c}$.

Let $\mathbf{a}=(1,0,1)$, $\mathbf{b}=(3,2,1)$, and $\mathbf{c}=(5,6,1)$. Compute $(\mathbf{b}-\mathbf{c})\times \mathbf{a}$.

Let $\mathbf{a} = \begin{pmatrix} 1 \\ 0 \\ 1 \end{pmatrix}$, $\mathbf{b} = \begin{pmatrix} 3 \\ 2 \\ 1 \end{pmatrix}$, and $\mathbf{c} = \begin{pmatrix} 5 \\ 6 \\ 1 \end{pmatrix}$.

Calculate $(2\mathbf{a} + 3\mathbf{b}) \times (\mathbf{b} - \mathbf{c})$.

Let $\mathbf{a}=(1,0,1)$ and $\mathbf{c}=(5,6,1)$. Calculate $\mathbf{c}\times \mathbf{a}$.

Let $\mathbf{a}=\begin{pmatrix} 1 \\ 0 \\ 1 \end{pmatrix}$, $\mathbf{b}=\begin{pmatrix} 3 \\ 2 \\ 1 \end{pmatrix}$, and $\mathbf{c}=\begin{pmatrix} 5 \\ 6 \\ 1 \end{pmatrix}$. Calculate $\mathbf{a}\times \mathbf{b}$.

Let $\mathbf{a}=\begin{pmatrix} 1 \\ 0 \\ 1 \end{pmatrix}$, $\mathbf{b}=\begin{pmatrix} 3 \\ 2 \\ 1 \end{pmatrix}$, and $\mathbf{c}=\begin{pmatrix} 5 \\ 6 \\ 1 \end{pmatrix}$. Verify the distributive law by simplifying $(\mathbf{a}+\mathbf{b})\times(\mathbf{b}+\mathbf{c})$ and comparing with $\mathbf{a}\times \mathbf{b} + \mathbf{a}\times \mathbf{c} + \mathbf{b}\times \mathbf{b} + \mathbf{b}\times \mathbf{c}$.

Let $a=(1,0,1)$, $b=(3,2,1)$, and $c=(5,6,1)$. Compute $b\times c$.

Let $\mathbf{a}=(1,0,1)$, $\mathbf{b}=(3,2,1)$, and $\mathbf{c}=(5,6,1)$. Compute the scalar triple product $\mathbf{a}\cdot(\mathbf{b}\times \mathbf{c})$.

Let $\mathbf{a} = \begin{pmatrix} 1 \\ 0 \\ 1 \end{pmatrix}$, $\mathbf{b} = \begin{pmatrix} 3 \\ 2 \\ 1 \end{pmatrix}$, and $\mathbf{c} = \begin{pmatrix} 5 \\ 6 \\ 1 \end{pmatrix}$. Calculate $\mathbf{a} \times (\mathbf{b} + \mathbf{c})$.

Let $\mathbf{a}=(1,0,1)$, $\mathbf{b}=(3,2,1)$, and $\mathbf{c}=(5,6,1)$. Compute $(\mathbf{a}\times \mathbf{b})+(\mathbf{b}\times \mathbf{c})+(\mathbf{c}\times \mathbf{a})$

Let $\mathbf{a}=\begin{pmatrix} 1 \\ 0 \\ 1 \end{pmatrix}$, $\mathbf{b}=\begin{pmatrix} 3 \\ 2 \\ 1 \end{pmatrix}$, and $\mathbf{c}=\begin{pmatrix} 5 \\ 6 \\ 1 \end{pmatrix}$. Find a unit vector perpendicular to both $(\mathbf{a}+\mathbf{b})$ and $(\mathbf{b}+\mathbf{c})$.

Let $\mathbf{a}=\begin{pmatrix} 1 \\ 0 \\ 1 \end{pmatrix}$, $\mathbf{b}=\begin{pmatrix} 3 \\ 2 \\ 1 \end{pmatrix}$, and $\mathbf{c}=\begin{pmatrix} 5 \\ 6 \\ 1 \end{pmatrix}$. Define $\mathbf{u}=\mathbf{a}+2\mathbf{c}$ and $\mathbf{v}=3\mathbf{b} - \mathbf{a}$.

Calculate $\mathbf{u}\times \mathbf{v}$.