In this question the unit vectors $i\mathbf{i}$ and $j\mathbf{j}$ are due east and due north respectively, and all distances are in kilometres.

At noon, ship $A\,$ is at the point $(4i+6j)(4\mathbf{i} + 6\mathbf{j})$ relative to a port $O$ , and moves with constant velocity $(3i−2j)(3\mathbf{i} - 2\mathbf{j})$ km h $^{-1}$ .

At the same time, ship $B\,$ is at the point $(−2i−4j)(-2\mathbf{i} - 4\mathbf{j})$ relative to $O$ , and moves with constant velocity $(6i+3j)(6\mathbf{i} + 3\mathbf{j})$ km h $^{-1}$ .

Write down, in terms of $t$ , the position vector of each ship $t\,$ hours after noon.

Show that the two ships collide, and state the time at which this happens.

In this question the unit vectors $i\mathbf{i}$ and $j\mathbf{j}$ are due east and due north respectively, and all distances are in kilometres.

At noon, ship $A\,$ is at the point $(4i+6j)(4\mathbf{i} + 6\mathbf{j})$ relative to a port $O$ , and moves with constant velocity $(3i−2j)(3\mathbf{i} - 2\mathbf{j})$ km h $^{-1}$ .

At the same time, ship $B\,$ is at the point $(−2i−4j)(-2\mathbf{i} - 4\mathbf{j})$ relative to $O$ , and moves with constant velocity $(6i+3j)(6\mathbf{i} + 3\mathbf{j})$ km h $^{-1}$ .

Write down, in terms of $t$ , the position vector of each ship $t\,$ hours after noon.

Show that the two ships collide, and state the time at which this happens.

1.10 Vectors

Question 16

Markscheme

1.10 Vectors

Question 16

Markscheme

1.10 Vectors

Question 16

1.10 Vectors Questions

1.10 Vectors

Question 16

1.10 Vectors Questions