Question

[20points][Precal] Find the cross product of -(3/4)V and (1/2)w if v = <-2, 12, -3> and w = <-7, 4, -6>

Answer 1

`\mathbf v=\langle-2,12,-3\rangle=-2\,\vec i+12\,\vec j-3\,\vec k`

`-\frac34\mathbf v=\frac32\,\vec i-9\,\vec j+\frac94\,\vec k`


`\mathbf w=\langle-7,4,-6\rangle=-7\,\vec i+4\,\vec j-6\,\vec k`

`\frac12\mathbf w=-\frac72\,\vec i+2\,\vec j-3\,\vec k`


`-\frac34\mathbf v*\frac12\mathbf w=\begin{vmatrix}\vec i&\vec j&\vec k\\\frac32&-9&\frac94\\-\frac72&2&-3\end{vmatrix}`

`=\left((-9)*(-3)-\frac94*2\right)\,\vec i-\left(\frac32*(-3)-\frac94*\left(-\frac72\right)\right)\,\vec j+\left(\frac32*2-(-9)*\left(-\frac72\right)\right)\,\vec k`

`=\frac{45}2\,\vec i-\frac{27}8\,\vec j-\frac{57}2\,\vec k=\left\langle\frac{45}2,-\frac{27}8,-\frac{57}2\right\rangle`