Unit 5 - Activity 7

ACTIVITY 5.7
COSINE OF THE ANGLE THAT TWO VECTORS FORM

We have two ways to calculate the scalar product of two vectorsand :

- if we know the modules || and || and the anglethat form, making the calculation
·= || || cos()

- if we know the components=(u₁,u₂) and =(v₁,v₂), we can make the calculation
                                                                ·= u₁v₁+ u₂v₂
Making equal, we have
                                                    || || cos() = u₁v₁+ u₂v₂
where we can isolate cos()

This last formula let us calculate the cosine of the angle that two vectors form knowing their components and, known cosine, to get the angle that they form.

Remember that the two modules || and || can be calculated from the components
.

INTERACTIVE ACTIVITY
Using
calculate the cosine of the angle that the next pair of vectors form. Draw vectors and check the result in the applet of the right side.

a) = (4,3)
     = (2,5)

b) = (5,3)
     = (-3,2)

c) = (2,-2)
     = (3,4)

d) = (4,1)
     = (-1,-2)

e) = (4,0)
     = (1,3)

f ) = (3,-2)
     = (-2,3)

g) = (3,2)
    = (-3,-2)

h) = (6,3)
    = (2,1)

i ) = (4,1)
     = (-1,4)

j ) = (3,0)
    = (0,-2)

牋牋牋牋牋牋牋牋牋牋牋牋SOLUTION

HOMEWORK

(Do you want a Word document prepared for making this work ?)

Like we have seen before, the formula

gives us the cosine of the angle that two vectors form. If, moreover, we want to calculate the angle that they form, shall use the function Arccosx that returns a comprised angle between 0º and 180º which has by cosine x (the button cos^-1 of the calculators). Then, using the calculator, calculate angles that form all pair of vectors

and

of the previous interactive activity.

END OF ACTIVITY 5.7
COSINE OF THE ANGLE THAT TWO VECTORS FORM

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