Question 3.6: Using Vector Information to Make a Graphical Representation ......
Using Vector Information to Make a Graphical Representation
A vector \vec{D} is given by \vec{D}=-3.5 \hat{\imath}+4.0 \hat{\jmath}. Draw a representation of \vec{D} as an arrow on an appropriate coordinate system.
INTERPRET and ANTICIPATE
Because the unit vectors \hat{\imath} \text { and } \hat{\jmath} are used, we need a two-dimensional x – y coordinate system.
SOLVE
Identify the vector components.
Draw a two-dimensional coordinate system with a suitable scale. The given vector is unitless, so do not show any units on the axes. Draw the vector components \vec{D}_x and \vec{D}_y on the coordinate system, placing the tail of \vec{D}_y at the head of \vec{D}_x (Fig. 3.32) \vec{D}_x is negative, pointing along the negative x axis. \vec{D}_y is positive, pointing parallel to the positive y axis. To find \vec{D}, add \vec{D}_x + \vec{D}_y using the head-to-tail method. The resultant vector is \vec{D}, as shown.
CHECK and THINK
It makes sense that vector \vec{D} points to the left and up because its x component is negative (left) and its y component is positive (up).
