Magnitude & Direction (AQA A-Level Mathematics): Quizzes

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Magnitude & Direction
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What is the formula for the magnitude of a 2D vector a=(a1a2)\mathbf{a} = \begin{pmatrix} a_1 \\ a_2 \end{pmatrix}?

∣a∣=a12+a22|\mathbf{a}| = \sqrt{a_1^2 + a_2^2}

For a 3D vector (a1a2a3)\begin{pmatrix} a_1 \\ a_2 \\ a_3 \end{pmatrix}, what is the magnitude formula?

a12+a22+a32\sqrt{a_1^2 + a_2^2 + a_3^2}

What is the magnitude of the vector (23)\begin{pmatrix} 2 \\ 3 \end{pmatrix}?

13\sqrt{13}

What is ∣x∣|\mathbf{x}| when x=(−2−4)\mathbf{x} = \begin{pmatrix} -2 \\ -4 \end{pmatrix}?

252\sqrt{5}

What formula gives the direction angle θ\theta with the positive xx-axis in 2D?

θ=tan⁡−1(a2a1)\theta = \tan^{-1}\left(\frac{a_2}{a_1}\right)

What is the direction of (32)\begin{pmatrix} 3 \\ 2 \end{pmatrix} (to 1 d.p.)?

33.7°33.7°

What is the direction of (−4−2)\begin{pmatrix} -4 \\ -2 \end{pmatrix} to 3 s.f.?

207°207°

What does the magnitude of a vector tell us?

How long the vector is

For a vector with magnitude 33 and direction 120°120°, what is the xx-component?

−32-\frac{3}{2}

For a vector with magnitude 33 and direction 120°120°, what is the yy-component?

332\frac{3\sqrt{3}}{2}

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