Vectors Quiz

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#4-1 Paper 1 Difficulty: Medium

Let $latex \vec{v}=\begin{pmatrix}
1\\
2\\
3
\end{pmatrix}$, and $latex \vec{w}=\begin{pmatrix}
-3\\
1\\
2
\end{pmatrix}$.

If $latex \vec{u}=\vec{v}-2\vec{w}$, find the magnitude of vector $latex \vec{u}$.

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#4-2 Paper 1 Difficulty: Medium

Let $latex \vec{u}=\begin{pmatrix} 3\\ k\\ -2 \end{pmatrix}$, and $latex \vec{v}=\begin{pmatrix} 5\\ -2\\ 7 \end{pmatrix}$, for $latex k>0$. The angle between $latex \vec{u}$ and $latex \vec{v}$ is $latex \frac{\pi }{2}$ radians.

Find the value of k.

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#4-3 Paper 1 Difficulty: Hard

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#4-4 Paper 1 Difficulty: Easy

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#4-5 Paper 2 Difficulty: Medium

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#4-6 Paper 1 Difficulty: Medium

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#4-7 Paper 2 Difficulty: Medium

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#4-8 Paper 2 Difficulty: Medium

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#4-9 Paper 2 Difficulty: Easy

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#4-10 Paper 1 Difficulty: Hard

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