IB Mathematics Applications & Interpretation Topic…

A survey drone releases a sensor pod. Its position vector relative to a fixed origin $O$ , at time $t$ seconds ( $t\ge0$ ), is described by $r(t)=\begin{pmatrix}6+5t \\ 9-3t \\ 12+7t-3t^2\end{pmatrix}$ , where the $z$ -axis is vertical and all distances are in metres.

that the sensor pod moves in a vertical plane and specify an equation of this plane.

a vector expression for the velocity of the sensor pod at time $t$ .

By calculating the scalar product, verify that the velocity of the sensor pod is orthogonal to the normal vector $3\mathbf{i}+5\mathbf{j}$ of this plane at all times.

Consider the vector $\vec{PQ} = \begin{pmatrix} 1 \\ 2 \\ 3 \end{pmatrix}$ .

a simplified algebraic expression for the dot product $u \cdot v$ in terms of $k$ .

Consider the vector $\vec{UV} = \begin{pmatrix} 1 \\ 1 \\ 2 \end{pmatrix}$ .

The points $A(1,2,-1)$ and $B(7,3,-4)$ are given.

Find a vector expression for the acceleration of the sensor pod at time $t$ .

the time when the sensor pod passes the point $(21,0,6)$ .

the speed of the sensor pod as it passes this point.

the magnitude $|\vec{PQ}|$ .

Given the vector $\vec{PR} = \begin{pmatrix} 3 \\ -1 \\ 2 \end{pmatrix}$ , the size of the angle .

the range of values for $k$ such that the angle between $u$ and $v$ is obtuse.

the magnitude $|\vec{UV}|$ .

Given the vector $\vec{UW} = \begin{pmatrix} 2 \\ 0 \\ 2 \end{pmatrix}$ , the size of the angle .

The line through $A$ and $B$ is perpendicular to the vector $(2,0,n)$ . Find the value of $n$ .

Find a vector equation of the line that passes through $A$ and $B$ .

IB Mathematics Applications & Interpretation AHL 3.13—scalar and Vector Products Questionbank

IB Mathematics Applications & Interpretation AHL 3.13—scalar and Vector Products Questionbank

IB Mathematics Applications & Interpretation AHL 3.13—scalar and Vector Products Questionbank

IB Mathematics Applications & Interpretation AHL 3.13—scalar and Vector Products Questionbank

IB Mathematics Applications & Interpretation (AI) Topic AHL 3.13—scalar and Vector Products Questionbank