Question

Use the figure to find each vector: u + v. Use vector notation as in Example 4.

Accepted Answer

Identify the components of vectors $$ \mathbf{u} $$ and $$ \mathbf{v} $$ from the figure. Typically, each vector can be broken down into its horizontal (x) and vertical (y) components. For example, $$ \mathbf{u} = (u_x, u_y) $$ and $$ \mathbf{v} = (v_x, v_y) . $$Write down the components of each vector explicitly. If the figure provides magnitudes and directions, use trigonometric functions to find components: $$ u_x = |\mathbf{u}| \cos 	heta_u $$, $$ u_y = |\mathbf{u}| \sin 	heta_u $$, and similarly for $$ \mathbf{v} . $$Add the corresponding components of the vectors to find the resultant vector $$ \mathbf{u} + \mathbf{v} $$: \ $$ \mathbf{u} + \mathbf{v} = (u_x + v_x, u_y + v_y) $$ Express the sum vector in vector notation, for example, $$ \mathbf{u} + \mathbf{v} = \langle u_x + v_x, u_y + v_y angle . If $$needed, interpret the resulting vector by calculating its magnitude and direction using: $$ |\mathbf{u} + \mathbf{v}| = \sqrt{(u_x + v_x)^2 + (u_y + v_y)^2} $$ and $$ 	heta = 	an^{-1} \left( \frac{u_y + v_y}{u_x + v_x} ight) $$ This completes the process of finding $$ \mathbf{u} + \mathbf{v} $$ using vector notation.

Use the figure to find each vector: u + v. Use vector notation as in Example 4.

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주요 개념

Vector Addition

Vector Notation

Graphical Representation of Vectors