Unghle

**Ortega** · February 12th 2009, 01:58 AM

Determine the unghle betwwen:
P1:x+y-z-1=0
P2:x+2y-7=0
when P=Plan

**running-gag** · February 12th 2009, 08:20 AM

Hi

One normal vector $\overrightarrow{n_1}$ to P1 has coordinates (1,1,-1) which are the coefficients of x, y and z in P1 equation

One normal vector $\overrightarrow{n_2}$ to P2 has coordinates (1,2,0)

The angle $\theta$ between P1 and P2 is the same as the one between $\overrightarrow{n_1}$ and $\overrightarrow{n_1}$

The dot product is
$\overrightarrow{n_1} \cdot \overrightarrow{n_2}=||\overrightarrow{n_1}|| \cdot ||\overrightarrow{n_1}|| \cdot \cos \theta$

Which gives
$3 = \sqrt{3} \: \sqrt{5} \: \cos \theta$

$\cos \theta = \frac{\sqrt{3}}{\sqrt{5}}$

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