Vectors (Advanced)

Vectors: core idea

• 1. Distance from point $(0,0,1)$ to plane $z=0$?

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• 2. Angle between planes $z=0$ and $x=0$ degrees?

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• 3. Shortest distance between skew lines? For $x$-axis and line $(0,1,0)+t(0,0,1)$: distance?

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• 4. Coplanar: points $(0,0,0),(1,0,0),(0,1,0),(1,1,a)$ for which $a$?

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• 5. Reflect $(0,0,1)$ across plane $z=0$: $z$-coordinate?

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• 6. Area of triangle $(0,0,0),(2,0,0),(0,2,0)$?

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• 7. If $\mathbf a\cdot\mathbf b=0$ and $|a|=|b|=2$, $|a\times b|$?

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• 8. Line through $(1,1,1)$ direction $\langle1,0,0\rangle$ meets plane $x=3$ at $x=$?

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• 9. Lagrange: $|a\times b|^2+|a\cdot b|^2$ for unit vectors equals?

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