A marine research vessel monitors the positions of underwater sensors relative to a coastal lighthouse located at a fixed origin $O$ .

Sensor $P\,$ is located at position vector

\overrightarrow{OP} = \begin{pmatrix} 4 \\ 1 \\ 3 \end{pmatrix}\text{ km}

Sensor $Q\,$ is deployed such that its displacement from sensor $P\,$ is given by

\overrightarrow{PQ} = \begin{pmatrix} 3 \\ 5 \\ -4 \end{pmatrix}\text{ km}

Determine the coordinates of sensor $Q$ .

A surface buoy $R\,$ is located at position vector

\overrightarrow{OR} = \begin{pmatrix} 1 \\ k \\ 2 \end{pmatrix}\text{ km}

where $k\,$ is a constant.

Given that the position vector of the buoy, $OR→\overrightarrow{OR}$ , is perpendicular to the displacement vector between sensor $Q\,$ and the buoy, $QR→\overrightarrow{QR}$ ,

find the possible values of $k$ .

A marine research vessel monitors the positions of underwater sensors relative to a coastal lighthouse located at a fixed origin $O$ .

Sensor $P\,$ is located at position vector

\overrightarrow{OP} = \begin{pmatrix} 4 \\ 1 \\ 3 \end{pmatrix}\text{ km}

Sensor $Q\,$ is deployed such that its displacement from sensor $P\,$ is given by

\overrightarrow{PQ} = \begin{pmatrix} 3 \\ 5 \\ -4 \end{pmatrix}\text{ km}

Determine the coordinates of sensor $Q$ .

A surface buoy $R\,$ is located at position vector

\overrightarrow{OR} = \begin{pmatrix} 1 \\ k \\ 2 \end{pmatrix}\text{ km}

where $k\,$ is a constant.

Given that the position vector of the buoy, $OR→\overrightarrow{OR}$ , is perpendicular to the displacement vector between sensor $Q\,$ and the buoy, $QR→\overrightarrow{QR}$ ,

find the possible values of $k$ .

1.10 Vectors

Question 93

Markscheme

1.10 Vectors

Question 93

Markscheme

1.10 Vectors

Question 93

1.10 Vectors Questions

1.10 Vectors

Question 93

1.10 Vectors Questions