Vector Basics flashcards: dot and cross product

Question 1

What is a vector (in $
R^n$) and how is it commonly written?

Accepted Answer

A vector is an ordered $n$-tuple of real numbers representing a directed quantity. It is commonly written as $\mathbf{v}=\langle v_1,\dots,v_nangle$ or as a column vector $\begin{pmatrix}v_1\ \vdots\ v_n\end{pmatrix}$.

Question 2

What is scalar multiplication of a vector $\mathbf{v}$ by a scalar $c$?

Accepted Answer

If $\mathbf{v}=\langle v_1,\dots,v_n\rangle$, then $$c\mathbf{v}=\langle cv_1,\dots,cv_n\rangle.$$

Question 3

State the cross product formula for $\mathbf{u}=\langle u_1,u_2,u_3\rangle$ and $\mathbf{v}=\langle v_1,v_2,v_3\rangle$.

Accepted Answer

$$\mathbf{u}	imes\mathbf{v}=\langle u_2v_3-u_3v_2,\;u_3v_1-u_1v_3,\;u_1v_2-u_2v_1angle$$ and $\|\mathbf{u}	imes\mathbf{v}\|=\|\mathbf{u}\|\,\|\mathbf{v}\|\sin	heta$.

Vector Basics flashcards: dot and cross product

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