NECO 2023 · Paper 1 · Q35

If $\mathbf{x} = 4\mathbf{i} + 5\mathbf{j}$ and $\mathbf{y} = -3\mathbf{i} + 4\mathbf{j}$ , find the modulus of $\mathbf{x} - \mathbf{y}$ .

Worked solution (try it first)

Subtract part by part: $\mathbf x - \mathbf y = (4 - (-3))\mathbf i + (5 - 4)\mathbf j$
$= 7\mathbf i + \mathbf j$ .
Its modulus is $\sqrt{7^2 + 1^2} = \sqrt{50}$ .
$\sqrt{50} = \sqrt{25 \times 2} = 5\sqrt2$ , option C.