http://www.ck12.org Chapter 7. Vectors
The formula for vector projection whereuis the onto vector is:
pro juv=(u·v
|u|) u
|u|=(< 1 , 3 >·< 5 , 1 >
√ 26
)< 5 , 1 >
√ 26
=
( 5 + 3
26
)
< 5 , 1 >
= 134 < 5 , 1 >
=<^2013 , 134 >
The graph confirms the result of the vector projection.
- First plot the two vectors and extend the “onto” vector. When the vector projection occurs, the vector<
− 2 , 2 >goes in the opposite direction of the vector< 4 ,− 2 >. This will create a vector projection going in the
opposite direction of< 4 ,− 2 >. - The box represents the girl and the sled. The blue arrow indicates the father’s 100 lb force. Notice that the
question asks for simply the amount of force which means scalar projection. Since this is not dependent on the
slope of this hill, we can rotate our perspective and still get the same scalar projection.