A formula that is used for the scalar projection of vec. x on vec. y can be simplified to IxIcos x. How can this be done?

Expert Answers
sciencesolve eNotes educator| Certified Educator

You should remember that the scalar projection of a vector represents the length of the vector projection, hence, projecting the vector `barx`  to the vector `bary`  yields:

`s = |x|*cos theta = x*bary`

Notice that `theta`  is the angle made by vector `barx`  to vector `bary`  and |x| expresses the length of vector `barx` .

You need to picture the vectors `barx`  and `bary`  and you need to project the vector `bar x`  to `bar y` . Notice that a right angle triangle is formed. You may evaluate the length of projection of vector `bar x`  on `bar y`  using  cosine function in right angle triangle.

`cos theta = s/|x| =gt s = |x|cos theta`

s expresses the adjacent side to angle `theta`

|x| represents the hypotenuse of right angle triangle

This value of scalar projection depends on the angle the vector `bar x`  makes to the vector`bar y`  such that:

`theta lt pi/2 =gt s = |x|`

`theta gt pi/2 =gt s = -|x|`