IB Mathematics Analysis and Approaches Question Type 1: Finding the Cross Product of Two Vectors Exercises

Compute the cross product of the vectors $\mathbf{a}=\left(\begin{array}{c}2\\ 3\\ 1\end{array}\right)$ and $\mathbf{b}=\left(\begin{array}{c}4\\ 1\\ 4\end{array}\right)$.

Find the cross product of $\mathbf{p}=(2,-1,3)$ and $\mathbf{q}=(4,0,2)$.

Find the cross product of $\mathbf{u}=\left(\begin{array}{c}1\\ 0\\ 0\end{array}\right)$ and $\mathbf{v}=\left(\begin{array}{c}0\\ 1\\ 0\end{array}\right)$.

Determine a vector perpendicular to $\left(\begin{array}{c}1\\ 2\\ 3\end{array}\right)$ and $\left(\begin{array}{c}4\\ 5\\ 6\end{array}\right)$.

Evaluate $(3,4,0)\times (0,0,5)$.

Compute the cross product of $\mathbf{p}=(1,0,2)$ and $\mathbf{q}=(3,1,1)$.

Determine whether $\mathbf{a}=\left(\begin{array}{c}1\\ 2\\ 3\end{array}\right)$ and $\mathbf{b}=\left(\begin{array}{c}2\\ 4\\ 6\end{array}\right)$ are parallel by computing $\mathbf{a}\times \mathbf{b}$.

Given $\mathbf{a}=\left(\begin{array}{c}2\\ 3\\ 4\end{array}\right)$ and $\mathbf{b}=\left(\begin{array}{c}-1\\ 0\\ 2\end{array}\right)$, find the magnitude $\Vert \mathbf{a}\times \mathbf{b}\Vert$.

Compute the area of the parallelogram spanned by $\mathbf{a}=\left(\begin{array}{c}2\\ 1\\ 3\end{array}\right)$ and $\mathbf{b}=\left(\begin{array}{c}-1\\ 2\\ 1\end{array}\right)$ by finding $\Vert \mathbf{a}\times \mathbf{b}\Vert$.

Find $(-1,2,5)\times (3,1,-2)$.

If $\mathbf{a}=(a,0,1)$ and $\mathbf{b}=(0,b,2)$, find $\mathbf{a}\times \mathbf{b}$ in terms of $a$ and $b$.

If $\mathbf{u}=(t,2,3)$ and $\mathbf{v}=(1,t,4)$, compute $\mathbf{u}\times \mathbf{v}$ in terms of $t$.