Vector-Vector Product

Practice Questions

Linear Algebra › Vector-Vector Product

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$\textbf{u},\textbf{v} , \textbf{w}, \textbf{x} \in \mathbb{R}^{3}$

Which of the following applies to $(\textbf{u} \times \textbf{v}) \times( \textbf{w} \times \textbf{x})$ , where " $\cdot$ " and " $\times$ " refer to the dot product and the cross product of two vectors?

$\textbf{u} = (1, x, x^{2}, x ^{3}, x^{4}, x^{5}, x^{6})$

$(x+ 1)^{6} = \textbf{u} \cdot \textbf{v}$ , where $\textbf{v}$ is which vector?

What is the physical significance of the resultant vector $\bf{C}$ , if $\bf{C}= \bf{A} \times \bf{B}$ ?

$\begin{align*}&\text{Find the vector product }\&\begin{bmatrix}1&-7&8&9&-9\end{bmatrix}\times\begin{bmatrix}-20\-8\-7\-2\-20\end{bmatrix}\end{align*}$

$\begin{align*}&\text{Find the product }A\times B \&\text{Where }A=\begin{bmatrix}18&-15&10&-15&-14&11\end{bmatrix}\text{ and }B=\begin{bmatrix}6\-5\-13\9\10\-8\end{bmatrix}\end{align*}$

$\begin{align*}&\text{Find the product }A\times B \&\text{Where }A=\begin{bmatrix}-18&12&-11&4&-19&13\end{bmatrix}\text{ and }B=\begin{bmatrix}-6\-2\-17\-20\-8\10\end{bmatrix}\end{align*}$

Calculate $\bf{A} \times \bf{B}$ , given

$\textbf{A}= 4\hat{i}-2\hat{j}$

$\textbf{B}= 1\hat{i}+3\hat{j}$

$\begin{align*}&\text{Find the vector product }\&\begin{bmatrix}-7&-6\end{bmatrix}\times\begin{bmatrix}11\-9\end{bmatrix}\end{align*}$

$\begin{align*}&\text{Find the product }A\times B \&\text{Where }A=\begin{bmatrix}13&-7&-14\end{bmatrix}\text{ and }B=\begin{bmatrix}-11\12\-4\end{bmatrix}\end{align*}$