IB Mathematics Applications & Interpretation Topic…

Consider three points $P(1,2,-1)$ , $Q(4,3,2)$ , and $R(0,-1,5)$ .

Find the vector $\overrightarrow{PQ}$ .

In a game animation, each vertex with position vector $\mathbf{r}$ is updated by $T:\mathbf{r}\mapsto\mathbf{r}'$ , where .

In a robotics simulation, each waypoint with position vector $\mathbf{r}$ is updated by $S:\mathbf{r}\mapsto\mathbf{r}'$ , where .

A geographic information system stores the outline of a lake as coordinate vectors in the $x$ - $y$ plane relative to a reference point $O$ . To compare two survey layers, the software applies the following three operations to every point on the outline:

an anticlockwise rotation about $O$ through radians

In a robotics drawing program, each point with position vector $\mathbf{r}$ is moved by $S:\mathbf{r}\mapsto\mathbf{r}'$ , where .

the dot product of vectors $\overrightarrow{PQ}$ and $\overrightarrow{PR}$ .

Find the cosine of the angle between $\overrightarrow{PQ}$ and $\overrightarrow{PR}$ .

Verify if the vectors are perpendicular.

the image of the point $(-4,3)$ under $T$ .

the coordinates $(u,v)$ of the point whose image is twice its position vector.

Let $R$ be a region in the plane. why the area of $T(R)$ is equal to the area of $R$ .

the image of the point $(3,-2)$ under $S$ .

the coordinates $(u,v)$ of the point whose image is twice its position vector.

Let $R$ be a region in the plane. why the area of $S(R)$ is equal to the area of $R$ .

the matrix for an anticlockwise rotation about $O$ through $\frac{\pi}{2}$ radians.

the matrix for a mirror reflection across the $y$ -axis.

the matrix for a clockwise rotation about $O$ through $\frac{\pi}{4}$ radians.

the composite matrix $\boldsymbol{T}$ that represents the resulting mapping by finding the product of these three matrices in the appropriate order.

$\boldsymbol{T}^2$ .

Hence what the value of $\boldsymbol{T}^2$ indicates about the final position of the outline if the complete sequence of operations is performed twice.

Consider three points $P, Q$ , and $R$ on the original outline. After the software applies the transformations, these points move to $P', Q'$ , and respectively.

the specific geometric transformation that corresponds to matrix $\boldsymbol{T}$ .

the image of the point $(-2,3)$ under $S$ .

the coordinates $(p,q)$ of the point whose image is twice its position vector.

Let $R$ be a region in the plane. why the area of $S(R)$ is equal to the area of $R$ .

IB Mathematics Applications & Interpretation AHL 3.9—matrix Transformations Questionbank

IB Mathematics Applications & Interpretation AHL 3.9—matrix Transformations Questionbank

IB Mathematics Applications & Interpretation AHL 3.9—matrix Transformations Questionbank

IB Mathematics Applications & Interpretation AHL 3.9—matrix Transformations Questionbank

IB Mathematics Applications & Interpretation (AI) Topic AHL 3.9—matrix Transformations Questionbank