[In this question the unit vectors $i\mathbf{i}$ and $j\mathbf{j}$ are due east and due north respectively.]

At time $t = 0$ , a particle $P\,$ is at position $(1i+3j)m(1\mathbf{i} + 3\mathbf{j})\text{m}$ relative to a fixed origin, $O$ .

The particle moves with velocity $(4i−8j)ms−1(4\mathbf{i} - 8\mathbf{j})\text{ms}^{-1}$

Find the speed of $P$ .

Show that $P\,$ passes through the point $A\,$ with position $(7i−9j)m(7\mathbf{i} - 9\mathbf{j})\text{m}$ .

[In this question the unit vectors $i\mathbf{i}$ and $j\mathbf{j}$ are due east and due north respectively.]

At time $t = 0$ , a particle $P\,$ is at position $(1i+3j)m(1\mathbf{i} + 3\mathbf{j})\text{m}$ relative to a fixed origin, $O$ .

The particle moves with velocity $(4i−8j)ms−1(4\mathbf{i} - 8\mathbf{j})\text{ms}^{-1}$

Find the speed of $P$ .

Show that $P\,$ passes through the point $A\,$ with position $(7i−9j)m(7\mathbf{i} - 9\mathbf{j})\text{m}$ .

Vectors

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