@?vectors

Flashcards 2022-01-25 What is the cross product useful for?? Finding a normal vector to two other vectors. What is another name for the cross product?? The vector product. Does the cross product give you a scalar or a vector answer?? A vector. How can you work out the direction of the cross product of two vectors?? Using the right hand rule. In the right hand rule for working out the direction of the cross product, what is the first vector $a$ represented by?

2021-01-14 What is the word explanation for the scalar/dot produt of two vectors?? The sum of the products of the components. What’s the notation for the dot product of $\pmb{a}$ and $\pmb{b}$?? $$ \pmb{a} \cdot \pmb{b} $$ What’s the sum formula for $\pmb{a} \cdot \pmb{b}$?? $$ \sum \pmb{a}_i \pmb{b}_i $$ $$ \left(\begin{matrix} 2 \ 2 \ 2 \end{matrix}\right) \cdot \left(\begin{matrix} 1 \ 2 \ 3 \end{matrix}\right) $$ What is the dot product of the two vectors?

2021-01-14 What is the general vector equation of a plane?? $$ \pmb{r} = \pmb{a} = \lambda\pmb{b} + \mu\pmb{c} $$ $$\pmb{r} = \pmb{a} = \lambda\pmb{b} + \mu\pmb{c}$$ What must be true about the two directional vectors $\pmb{b}$ and $\pmb{c}$?? They are not parallel to one another. What equation does this photo represent?? $$ \pmb{r} = \pmb{a} = \lambda\pmb{b} + \mu\pmb{c} $$ $$ \left(\begin{matrix} 3+2\lambda+\mu \ 4+\lambda-\mu \ -2+\lambda+2\mu \end{matrix}\right) = \left(\begin{matrix} 2 \ 2 \ -1 \end{matrix}\right)$$ How could you rewrite this?

2021-01-11 What is the vector equation for a straight line?? $$ \pmb{r} =\pmb{a} + \lambda \pmb{b} $$ $$\pmb{r} =\pmb{a} + \lambda \pmb{b}$$ What is the variable $\pmb{a}$ called?? The position vector. $$\pmb{r} =\pmb{a} + \lambda \pmb{b}$$ What is the variable $\pmb{b}$ called?? The direction vector. $$\pmb{r} =\pmb{a} + \lambda \pmb{b}$$ What is the variable $\pmb{r}$ called?? The general position vector for a point on the line. $$\pmb{r} =\pmb{a} + \lambda \pmb{b}$$ What is the informal name for $\lambda$ called here?

See also: [[Further Maths - Vector Equation of a Line]]S [[Further Maths - Vector Equation of a Plane]]S [[Further Maths - Dot Product]]S What is the formula for the distance to a three dimensional point $(a,b,c)$?? $$ \sqrt{a^2 + b^2 + c^2} $$ $$ \left(\begin{matrix} a \ b \ c \end{matrix}\right) $$ What is the formula for the length of the vector?? $$ \sqrt{a^2 + b^2 + c^2} $$