Vector question

**daphnewoon** · October 24th 2009, 08:11 AM

3. Use cross product to find the sine of the angle between the vectors

u (2, 3, -6)

v (2, 3, 6)

**Soroban** · October 24th 2009, 08:48 AM

Hello, daphnewoon!

1. Giiven the points: . $O:(0, 0, 0),\;P:(2, 6, \text{-}1),\;Q:(1, 1, 1),\; R(4, 6, 2)$

Find a vector $\vec{n}$ that is perpendicular to both $\overrightarrow{PQ}$ and $\overrightarrow{OR}.$

We have: . $\begin{array}{ccc}\overrightarrow{PQ} &=& \langle \text{-}1,\text{-}5,2\rangle \\ \overrightarrow{OR} &=& \langle 4,6,2\rangle \end{array}$

Then: . $\vec{n} \;=\;\overrightarrow{PQ} \times \overrightarrow{OR} \;=\;\left|\begin{array}{ccc}i&j&k \\ \text{-}1& \text{-}5 & 2\\4 & 6 & 2\end{array}\right| \;=\;\text{-}22i + 10j + 14k \;=\;\langle 11,\text{-}5,\text{-}7\rangle$

**daphnewoon** · October 24th 2009, 08:52 AM

THank you, soroban for replying.

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