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Question Number 119315 by zakirullah last updated on 23/Oct/20

Answered by ebi last updated on 23/Oct/20

$$AB=\lambda CD,where\lambda isaconstant.$$$$AB=\left(\begin{array}{c}3-2\\ 1-(-1)\\ 0-1\end{array}\right)=\left(\begin{array}{c}1\\ 2\\ -1\end{array}\right)$$$$CD=\left(\begin{array}{c}-1-2\\ -2-4\\ 1-(-2)\end{array}\right)=\left(\begin{array}{c}-3\\ -6\\ 3\end{array}\right)$$$$\therefore \left(\begin{array}{c}1\\ 2\\ -1\end{array}\right)=\left(\begin{array}{c}-3\\ -6\\ 3\end{array}\right)$$$$\left(\begin{array}{c}1\\ 2\\ -1\end{array}\right)=-3\left(\begin{array}{c}1\\ 2\\ -1\end{array}\right)$$$$AB=-3CD$$

Commented by zakirullah last updated on 23/Oct/20

$$\mathit{v}\mathit{e}\mathit{r}\mathit{y}\mathit{g}\mathit{r}\mathit{e}\mathit{a}\mathit{t}\mathit{f}\mathit{u}\mathit{l}\mathit{l}\mathit{w}\mathit{o}\mathit{r}\mathit{k}$$

Answered by 1549442205PVT last updated on 24/Oct/20

$$\mathrm{We}\mathrm{have}\mathrm{A}(2,-1,1),\mathrm{B}(3,1,0),\mathrm{C}(2,4,-2)$$$$\mathrm{and}\mathrm{D}(-1,-2,1)$$$$\Rightarrow \overrightarrow{\mathrm{AB}}=(1,2,-1),\overrightarrow{\mathrm{CD}}=(-3,-6,3)$$$$\Rightarrow \overrightarrow{\mathrm{CD}}=(-3)\overrightarrow{\mathrm{AB}}\Rightarrow \overrightarrow{\mathrm{AB}}//\overrightarrow{\mathrm{CD}}(\mathbf{q}.\mathbf{e}.\mathbf{d})$$

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