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.

1.13 J: Vectors

Question 6

Markscheme

1.13 J: Vectors

Question 6

Markscheme

1.13 J: Vectors

Question 6

1.13 J: Vectors Questions

1.13 J: Vectors

Question 6

1.13 J: Vectors Questions