# 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?

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### 1 Answer

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|`

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