Question Type 1: Finding the cross product of two vectors Bootcamps

Find the cross product of $\mathbf{u} = (1,0,0)$ and $\mathbf{v} = (0,1,0)$.

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

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

Compute the cross product of the vectors $\mathbf{a} = (2,3,1)$ and $\mathbf{b} = (4,1,4)$.

Determine whether $\mathbf{a}=(1,2,3)$ and $\mathbf{b}=(2,4,6)$ are parallel by computing $\mathbf{a}\times\mathbf{b}$.

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

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

Compute the area of the parallelogram spanned by $\mathbf{a}=(2,1,3)$ and $\mathbf{b}=(-1,2,1)$ by finding $\|\mathbf{a}\times\mathbf{b}\|$.

Given $\mathbf{a}=(2,3,4)$ and $\mathbf{b}=(-1,0,2)$, find the magnitude $\|\mathbf{a}\times\mathbf{b}\|$.

Determine a vector perpendicular to $(1,2,3)$ and $(4,5,6)$.

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

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