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 expressed in component form as $$ \mathbf{u} = \langle u_x, u_y \rangle $$ and $$ \mathbf{v} = \langle v_x, v_y \rangle $$, where $$ u_x $$ and $$ u_y $$ are the horizontal and vertical components of $$ \mathbf{u} $$, and similarly for $$ \mathbf{v} . $$Recall that vector subtraction $$ \mathbf{u} - \mathbf{v}  is $$performed by subtracting the corresponding components of $$ \mathbf{v} $$ from $$ \mathbf{u} . $$This means $$ \mathbf{u} - \mathbf{v} = \langle u_x - v_x, u_y - v_y \rangle . $$Calculate the horizontal component of $$ \mathbf{u} - \mathbf{v}  by $$subtracting the horizontal component of $$ \mathbf{v} $$ from that of $$ \mathbf{u} $$: $$ u_x - v_x . $$Calculate the vertical component of $$ \mathbf{u} - \mathbf{v}  by $$subtracting the vertical component of $$ \mathbf{v} $$ from that of $$ \mathbf{u} $$: $$ u_y - v_y . $$Write the resulting vector in component form as $$ \mathbf{u} - \mathbf{v} = \langle u_x - v_x, u_y - v_y \rangle $$, which is the vector notation requested.

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

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Key Concepts

Vector Subtraction

Vector Notation

Graphical Representation of Vectors