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Why is mass a scalar rather than a vector?

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Mass has magnitude but no direction.

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What movement does $\\begin{pmatrix}6\\\\-4\\end{pmatrix}$ represent?

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6 units right and 4 units down.

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Find $\\overrightarrow{AB}$ for $A(-2,3)$ and $B(4,-1)$.

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$\\begin{pmatrix}6\\\\-4\\end{pmatrix}$

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What vector results if the subtraction for $\\overrightarrow{AB}$ is reversed?

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$\\overrightarrow{BA}$, which points in the opposite direction.

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For $\\mathbf v=\\begin{pmatrix}x\\\\y\\end{pmatrix}$, its magnitude is $\\text{[...]}$.

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For $\\mathbf v=\\begin{pmatrix}x\\\\y\\end{pmatrix}$, its magnitude is $\\boxed{\\sqrt{x^2+y^2}}$.

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Find the magnitude of $\\begin{pmatrix}-5\\\\12\\end{pmatrix}$.

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$13$

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Why do negative components contribute positively to magnitude?

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The components are squared.

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How should $\\sqrt{13}$ be reported if no decimal is requested?

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Leave it as the exact surd $\\sqrt{13}$.

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From where and in which direction is a vector's direction angle normally measured?

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Anticlockwise from the positive $x$-axis.

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Which quadrant contains $\\begin{pmatrix}-3\\\\4\\end{pmatrix}$?

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Quadrant II

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The reference angle for components $x$ and $y$ is $\\text{[...]}$.

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The reference angle for components $x$ and $y$ is $\\boxed{\\tan^{-1}\\left(\\frac{|y|}{|x|}\\right)}$.

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Why can $\\tan^{-1}(y/x)$ give the wrong direction angle?

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It gives a principal value that may not identify the correct quadrant.

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In Quadrant II, the direction angle is $\\text{[...]}$.

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In Quadrant II, the direction angle is $\\boxed{\\theta=180^\\circ-\\alpha}$.

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In Quadrant III, the direction angle is $\\text{[...]}$.

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In Quadrant III, the direction angle is $\\boxed{\\theta=180^\\circ+\\alpha}$.

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Why is the direction of $\\begin{pmatrix}0\\\\0\\end{pmatrix}$ undefined?

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It does not point anywhere.

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Find the direction of $\\begin{pmatrix}-3\\\\4\\end{pmatrix}$ to $1$ decimal place.

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$126.9^\\circ$

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For magnitude $r$ and direction $\\theta$, the horizontal component is $\\text{[...]}$.

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For magnitude $r$ and direction $\\theta$, the horizontal component is $\\boxed{x=r\\cos\\theta}$.

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For magnitude $r$ and direction $\\theta$, the vertical component is $\\text{[...]}$.

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For magnitude $r$ and direction $\\theta$, the vertical component is $\\boxed{y=r\\sin\\theta}$.

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Find the horizontal component of a vector with magnitude $10$ and direction $210^\\circ$.

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$-5\\sqrt{3}$

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Find the vertical component of a vector with magnitude $10$ and direction $210^\\circ$.

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$-5$

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