Questions and Answers
What are the direction cosines of a vector in three-dimensional Euclidean space?
\alpha = \frac{v_x}{\sqrt{v_x^2 + v_y^2 + v_z^2}}, \beta = \frac{v_y}{\sqrt{v_x^2 + v_y^2 + v_z^2}}, \gamma = \frac{v_z}{\sqrt{v_x^2 + v_y^2 + v_z^2}}
What do the direction cosines represent?
The contributions of each component of the basis to a unit vector in that direction
How are the direction cosines related to the components of the vector?
\alpha = \frac{v_x}{\sqrt{v_x^2 + v_y^2 + v_z^2}}, \beta = \frac{v_y}{\sqrt{v_x^2 + v_y^2 + v_z^2}}, \gamma = \frac{v_z}{\sqrt{v_x^2 + v_y^2 + v_z^2}}
If v is a Euclidean vector in three-dimensional space given by $v = 3i - 4j + 5k$, what are the direction cosines?
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What are the direction cosines of a unit vector in the direction of the positive x-axis?
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