Find the angle theta between u=< 7,-2> and v=< -1,2>

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

step-by-step explanation:

you can add the two numbers and divide the result by 2. or you can find the gap between the two numbers and add half of this to the smaller number.

dont trust me im no expert these losers made me fail a test bro this sucks

step-by-step explanation: