Bheactoran geoimeatrach test questions

1

\(P=(2,1, - 3)\) agus \(Q= (8, - 4,5)\). Dè th' ann am \(\overrightarrow {PQ}\)?

\[\left(\begin{array}{l}\,\,\,\,6\\\,\,\,\,0\\- 3 \end{array}\right)\]

\[ \left( \begin{array}{l}\,\,\,\,\,6\\-5\\\,\,\,\,8\end{array}\right)\]

\[\left(\begin{array}{l}- 6\\\,\,\,\,\,5\\ -8 \end{array}\right)\]

2

\(P = (0,1, - 5)\) agus \(\overrightarrow{PQ}=\left(\begin{array}{l}\,\,\,\,\,6\\-1\\\,\,\,\,2\end{array}\right) \).

Dè na co-chomharran a tha aig Q?

\[( - 6,2, - 7)\]

\[(6,0, - 3)\]

\[(6,2, - 7)\]

3

\(Q = (4, - 2,1)\) agus \(\overrightarrow {PQ} = \left( \begin{array}{l}3\\2\\1\end{array} \right)\).

Dè na co-chomharran a tha aig P?

\[(1, - 4,0)\]

\[( - 1,4,0)\]

\[(7,0,2)\]

4

\(\overrightarrow{PQ} = \left( \begin{array}{l}\,-1\\\,\,\,\,\,4\\-2\end{array} \right)\).

Dè a' mheudachd aig \(\overrightarrow {PQ}\)?

\[\sqrt 8\]

\[\sqrt {11}\]

\[\sqrt {21}\]

5

Ma tha na puingean \(T(2, - 1)\), \(U( - 1,1)\) agus \(V(k,3)\) air an aon loidhne dhìrich, tha \(k\) co-ionann ri:

\[- 3\]

\[- 4\]

\[3\]

6

Tha \(A(1,2,1)\), \(B(4,5,6)\) agus \(C(10,y,16)\) co-loidhneach. Dè an luach a th' aig y?

\[8\]

\[3\]

\[11\]

7

Tha \(A(4, - 2,0)\), \(B(10,7,3)\) agus \(C(14,13,5)\) co-loidhneach. Dè an co-mheas anns a bheil \(B\) a' roinn \(AC\)?

\[1:2\]

\[2:3\]

\[3:2\]

8

\(A = (1, - 2,4)\) agus \(B = (8,12, - 3)\). Obraich a-mach na co-chomharran aig \(AB\) anns a' cho-mheas \(2:5\).

\[(3,2,2)\]

\[(3, - 2,2)\]

\[(3, - 2, - 2)\]

9

Obraich a-mach an ceàrn \(PQR\) far a bheil \(\overrightarrow{QP}=\left(\begin{array}{l}4\\0\\3\end{array}\right)\) agus \(\overrightarrow{QR}=\left(\begin{array}{l}\,\,\,\,\,0\\-3\\-4\end{array}\right)\).

\[61.3^\circ\]

\[118.3^\circ\]

\[- 118.3^\circ\]

10

Obraich a-mach luach \(a.(b+c)\) far a bheil \(a=\left(\begin{array}{l}\,\,\,\,6\\-1\\\,\,\,0\end{array}\right)\), \(b = \left(\begin{array}{l}2\\1\\3\end{array}\right)\) agus \(c =\left(\begin{array}{l}\,\,\,\,\,0\\\,\,\,\,\,1\\-1\end{array}\right)\)

\[8\]

\[12\]

\[10\]