# Math Help - Vector Problem with Picture

1. ## Vector Problem with Picture

AP and BQ are altitudes of triangle ABC. Let
<above sym=rarr>OA</above> = p
<above sym=rarr>OB</above> = q
<above sym=rarr>OC</above> = r

1. Find vector expressions for <above sym=rarr>AC</above> and
<above sym=rarr>BC</above> in terms of p, q, and r.

2. Deduce that q x r = p x q = p x r

3. Hence, prove that OC is perpendicular to AB.

2. Originally Posted by SunshineJx

AP and BQ are altitudes of triangle ABC. Let
<above sym=rarr>OA</above> = p
<above sym=rarr>OB</above> = q
<above sym=rarr>OC</above> = r

1. Find vector expressions for <above sym=rarr>AC</above> and
<above sym=rarr>BC</above> in terms of p, q, and r.

2. Deduce that q x r = p x q = p x r

3. Hence, prove that OC is perpendicular to AB.

1. $AC = AO + OC$
$= -OA + OC$
$= OC - OA$
$= \mathbf{r} - \mathbf{p}$.