Tuilleadh eisimpleirean de bheactoran ùra (toradh)

Eisimpleir

Ma tha \(P(1,4,8)\) agus \(Q( - 3,1, - 4)\), obraich a-mach \(\overrightarrow {PQ}\).

Gus seo a dhèanamh, smaoinich gu bheil thu san t-suidheachadh aig puing \(P\). Cia mheud aonad a dh'fheumadh tu siubhal gach taobh mus ruigeadh tu puing \(Q\)? 'S e dòigh luath air seo a dhèanamh ma bheir thu luach nan co-chomharran aig \(P\) air-falbh bho na co-chomharran aig \(Q\).

\[\overrightarrow {PQ} = \left( \begin{array}{l}- 3 - 1\\ \,\,\,\,\,1 - 4\\- 4 - 8\end{array} \right) = \left( \begin{array}{l}\,\,\,- 4\\\,\,\,- 3\\- 12\end{array} \right)\]

Feuch gun toir thu air-falbh na co-chomharran ceart. Bhiodh am freagairt gu math eadar-dhealaichte nan toireadh tu \(Q\) air-falbh bho \(P\)

Mar sin tha e fìor gun tèid agad air co-chomharran puing obrachadh a-mach ma tha fios agad air na co-chomharran aig puing eile agus a' bheactor a tha gan ceangal.

Eisimpleir

Ma tha \(P(1,4,10)\) agad agus \(\overrightarrow {PQ}\) a' riochdachadh bheactor \(u =\left(\begin{array}{l}\,\,\,\,\,2\\\,\,\,\,\,1\\- 1\end{array} \right)\) obraich a-mach \(Q\).

\(\left(\begin{array}{l}\,\,\,\,\,2\\\,\,\,\,\,1\\- 1\end{array} \right)\) a' ciallachadh \(\left( \begin{array}{l}meudaich\,x\,le\, 2\\meudaich\,y\,le\, 1\\beagaich\,z\,le\, 1\end{array} \right)\)

Mar sin ma tha \(P = (1,4,10)\) tha \(Q = (3,5,9)\)

'S e a' bheactor suidheachaidh a' bheactor bhon origin gu \(P\).

Ma tha \(P = (3,4, - 2)\), can, an uair sin tha \(\overrightarrow {OP} = \left( \begin{array}{l}\,\,\,\,\,3\\\,\,\,\,\,4\\- 2 \end{array} \right)\)

'S e \(\overrightarrow {OP}\) a' bheactor suidheachaidh aig \(P\). Bidh sinn a' sgrìobhadh \(\textbf{p} = \left( \begin{array}{l}\,\,\,\,\,3\\\,\,\,\,\,4\\- 2\end{array} \right)\)

Ma tha \(\overrightarrow {PQ} = \left( \begin{array}{l}\,\,\,\,\,5\\\,\,\,\,\,4\\- 2\end{array} \right)\) bidh an fhaid no a' mheudachd aig \(\overrightarrow {PQ}\), sgrìobhte mar \(\left| {\overrightarrow {PQ} } \right|\), air a thoirt mar:

\[\left| {\overrightarrow {PQ} } \right| = \sqrt {{5^2} + {4^2} + {{( - 2)}^2}} = \sqrt {45}=3\sqrt {5}\]