IB Mathematics Applications & Interpretation Topic…

The point $P$ lies on the line segment joining points $A(2,1)$ and $B(10,5)$ such that $\overrightarrow{A P}=\frac{3}{4} \overrightarrow{A B}$ .

Find the position vector of $P$ and its distance from the origin.

A survey drone is monitored from a fixed launch point. Its position relative to the launch point at time $t$ seconds is given by $r=\begin{pmatrix}9\\-12\\20\end{pmatrix}+t\begin{pmatrix}0.6\\-0.8\\2.4\end{pmatrix}$ . The components represent easting (m), northing (m), and height above the launch point (m).

(a) the speed of the drone.

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

(b) Given the vector $\vec{PR} = \begin{pmatrix} 3 \\ -1 \\ 2 \end{pmatrix}$ , the size of the angle $Q\hat{P}R$ .

A drone in a warehouse travels in a straight line through points $C(-1,3,6)$ and $D(1,2,8)$ , measured from the corner $O$ of the building. The plane $y=0$ represents a side wall and the $z$ -axis points vertically upwards. Distances are given in metres. The drone continues along the same path until it meets the wall at point $Q$ .

(a) a vector equation for the path followed by the drone.

A laser beam in a gallery travels in a straight line through points $A(4,-2,5)$ and $B(1,4,2)$ , measured from a fixed reference point $O$ on the floor. The $xy$ -plane represents the floor and the $z$ -axis points vertically upwards. Distances are given in metres. The beam continues until it meets the floor at point $P$ .

(a) a vector equation for the path followed by the beam.

(b) the distance of the drone from the launch point when $t=0$ .

(a) the magnitude $|\vec{PQ}|$ .

(b) the coordinates of point $Q$ .

(b) the coordinates of point $P$ .

IB Mathematics Applications & Interpretation AHL 3.10—vector Definitions Questionbank

IB Mathematics Applications & Interpretation AHL 3.10—vector Definitions Questionbank

IB Mathematics Applications & Interpretation AHL 3.10—vector Definitions Questionbank

IB Mathematics Applications & Interpretation AHL 3.10—vector Definitions Questionbank

IB Mathematics Applications & Interpretation (AI) Topic AHL 3.10—vector Definitions Questionbank