Direction Cosines and Euclidean Space Quiz

\alpha = \frac{v_x}{v_x^2 - v_y^2 - v_z^2}, \beta = \frac{v_y}{v_x^2 - v_y^2 - v_z^2}, \gamma = \frac{v_z}{v_x^2 - v_y^2 - v_z^2}

\alpha = \frac{v_x}{v_x^2 \cdot v_y^2 \cdot v_z^2}, \beta = \frac{v_y}{v_x^2 \cdot v_y^2 \cdot v_z^2}, \gamma = \frac{v_z}{v_x^2 \cdot v_y^2 \cdot v_z^2}

\alpha = \frac{v_x}{v_x^2 + v_y^2 + v_z^2}, \beta = \frac{v_y}{v_x^2 + v_y^2 + v_z^2}, \gamma = \frac{v_z}{v_x^2 + v_y^2 + v_z^2}

\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}} (correct)

The angles between the vector and the three negative coordinate axes

The distances from the origin to the end of the vector

The magnitudes of the vector components

The contributions of each component of the basis to a unit vector in that direction (correct)

\alpha = v_x^2, \beta = v_y^2, \gamma = v_z^2

\alpha = v_x, \beta = v_y, \gamma = v_z

\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}} (correct)

\alpha = \frac{v_x}{v_x^2 + v_y^2 + v_z^2}, \beta = \frac{v_y}{v_x^2 + v_y^2 + v_z^2}, \gamma = \frac{v_z}{v_x^2 + v_y^2 + v_z^2}

<p>\alpha = \frac{3}{\sqrt{50}}, \beta = \frac{-4}{\sqrt{50}}, \gamma = \frac{5}{\sqrt{50}}</p> Signup and view all the answers

<p>\alpha = 1, \beta = 0, \gamma = 0</p> Signup and view all the answers