# Vectors Quiz

## Make sure to try these on a piece of paper first

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 $latex \vec{u}$.

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.

**This question is part of theMath SL Online Revision Course**

(but keep in mind that at least the first question of each topic is free!)

**This question is part of theMath SL Online Revision Course**

(but keep in mind that at least the first question of each topic is free!)

**This question is part of theMath SL Online Revision Course**

(but keep in mind that at least the first question of each topic is free!)

**This question is part of theMath SL Online Revision Course**

(but keep in mind that at least the first question of each topic is free!)

**This question is part of theMath SL Online Revision Course**

(but keep in mind that at least the first question of each topic is free!)

**This question is part of theMath SL Online Revision Course**

(but keep in mind that at least the first question of each topic is free!)

**This question is part of theMath SL Online Revision Course**

(but keep in mind that at least the first question of each topic is free!)

**This question is part of theMath SL Online Revision Course**

(but keep in mind that at least the first question of each topic is free!)