In a high-precision manufacturing bay, a robotic arm maps the positions of three docking pins relative to a fixed calibration origin $O$ . The pins have the following position vectors:

$∙\bullet$ Pin $P$ has position vector $4i−j+2k4\mathbf{i} - \mathbf{j} + 2\mathbf{k}$ $∙\bullet$ Pin $Q$ has position vector $6i+3j−2k6\mathbf{i} + 3\mathbf{j} - 2\mathbf{k}$ $∙\bullet$ Pin $R$ has position vector $ki+3j+5kk\mathbf{i} + 3\mathbf{j} + 5\mathbf{k}$

where $k$ is a constant.

The guide rail $L$ is a straight line passing through the centers of pins $P$ and $Q$ .

Determine a vector equation for the line $L$ .

Given that the displacement vector $PR⃗\vec{PR}$ is perpendicular to the guide rail $L$ ,

find the value of $k$ .

Calculate the area of the triangular space $P QR$ formed by the pins, expressing your answer as a surd in its simplest form.

In a high-precision manufacturing bay, a robotic arm maps the positions of three docking pins relative to a fixed calibration origin $O$ . The pins have the following position vectors:

where $k$ is a constant.

The guide rail $L$ is a straight line passing through the centers of pins $P$ and $Q$ .

Determine a vector equation for the line $L$ .

Given that the displacement vector $PR⃗\vec{PR}$ is perpendicular to the guide rail $L$ ,

find the value of $k$ .

Calculate the area of the triangular space $P QR$ formed by the pins, expressing your answer as a surd in its simplest form.

1.11 Vectors

Question 39

Markscheme

1.11 Vectors

Question 39

Markscheme

1.11 Vectors

Question 39

1.11 Vectors Questions

1.11 Vectors

Question 39

1.11 Vectors Questions