Thursday, October 27, 2011

Find the magnitude and the direction angle

Find the magnitude and the direction angle (to the nearest tenth) for the vector
\f[\left<3, 3 \right>\f]
1. Magnitude:
Formula: 
\f[\left|\left|v \right| \right|=\sqrt{x^{2}+y^{2}}\f]
\f[\left|\left|3, 3 \right| \right| = \sqrt{3^{2}+3^{2}} = \sqrt{9+9}=\sqrt{18}= 3\sqrt{2}\f]

2. Direction Angle:
Formula: 
\f[\theta = \tan^{-1} \frac{y}{x}\f]
Graph the vector:
Find the direction angle:\f[\tan \theta =\frac{3}{3} = 1\f]
\f[\tan^{-1} (1) = 45\deg \f]
Final results:
Magnitude 3√2
Direction angle 45 °

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