Answer:
a) 0°
b) 180°
c) 90°
Explanation:
Hello!
To solve this question let a be the vector whose length is 15 m and b the vector of length 20 m
So:
|a | = 15
|b | = 20
Since we are looking for the angle between the vectors we need to calculate the length of the sum of the two vectors, this is:
[tex]|a+b|^{2} = |a|^{2} + |b|^{2} + 2 |a||b|cos(\theta)[/tex]
Now we replace the value of the lengths:
[tex]|a+b|^{2} = 15^{2} + 20^{2} + 2*15*20*cos(\theta)[/tex]
[tex]|a+b|^{2} = 625 + 600*cos(\theta)[/tex] --- (1)
Now, if:
a) |a+b| = 35
First we can see that 20 + 15 = 35, so the angle must be 0, lets check this:
[tex]35^{2} = 625 + 600*cos(\theta)[/tex]
[tex]1225 = 625 + 600*cos(\theta)[/tex]
[tex]600 = 600*cos(\theta)[/tex]
[tex]1= cos(\theta)[/tex]
and :
[tex]\theta = arccos(1)[/tex]
θ = 0
b) |a+b|=5
From eq 1 we got:
[tex]\theta = arccos(\frac{|a+b|^{2}-625}{600})[/tex] --- (2)
[tex]\theta = arccos(\frac{|a+b|^{2}-625}{600})[/tex]
[tex]\theta = arccos(-1)[/tex]
θ = π or θ = 180°
c) |a+b|=25
[tex]\theta = arccos(\frac{|25|^{2}-625}{600})[/tex]
[tex]\theta = arccos(-1)[/tex]
θ = π/2 or θ = 90°
