Answer:
Ф=2.3127 radians
Step-by-step explanation:
Apply the equation for dot product of two vectors;
u.v=║u║×║v║cosФ--------------------------------------(1)
where;
u=vector u
v=vector v
║u║=magnitude of vector u
║v║=magnitude of vector v
Ф=theta, angle between vector u and vector v
Given
u=<7,-2>
v=<-1,2>
Find dot product u.v= (7)(-1) + (-2)(2) =-7+-4 =-11
Find magnitude of vector;
║u║=√(7²+-2²)=√(49+4)=√53
Find magnitude of vector v
║v║=√ -1²+2²=√1+4 =√5
Finding value of Ф from equation 1
Ф=cos⁻¹(u*v / ║u║*║v║)
Ф=cos⁻¹(-11/(√5 ×√53) )
Ф= cos⁻¹ (-11÷16.28)
Ф= cos⁻¹ (-0.67572462851)
Ф=2.3127 radians
