Vectors: Question 6

Worked solution

Step 1: Square and sum the components

$|\mathbf{v}| = \sqrt{2^2 + (-3)^2 + 6^2} = \sqrt{4 + 9 + 36} = \sqrt{49} = 7$

Step 2: Recompute independently as a check

Reordering the sum: $6^2 + 2^2 + (-3)^2 = 36 + 4 + 9 = 49$, so $|\mathbf{v}| = \sqrt{49} = 7$ again, the same result.

Why the other options are wrong

• B: comes from stopping at $49$ under the square root sign and forgetting to take the square root.
• C: comes from adding the components directly, $2 + (-3) + 6 = 5$, instead of squaring, summing and square-rooting.
• D: comes from omitting the $\mathbf{j}$-component from the sum, $\sqrt{2^2+6^2} = \sqrt{4+36} = \sqrt{40} = 2\sqrt{10}$.

Final answer

$\boxed{|\mathbf{v}| = 7} \quad \text{(Option A)}$