The angle between two vectors is:
CosФ = u - v / Magnitude(u) x magnitude(v)
Magnitude of u = SQRT(7^2 + -2^2) = SQRT(49 +4) = SQRT(53)
Magnitude of v = SQRT(-1^2 +2^2) = SQRT(1 +4) = SQRT(5)
u x v = (7 x -1) + (-2 x 2) = -7 + -4 = -11
cosФ = -11 / sqrt(53) x sqrt(5)
cosФ = -11sqrt265) / 265
Ф =cos^-1(-11sqrt265) / 265)
Ф=132.51 degrees.
The angle between the two vectors u = <7, –2> and v = <–1, 2>. is 132.51 degrees.
It is defined as the quantity that has magnitude as well as direction also the vector always follows the sum triangle law.
It is given that:
Two vectors are:
u = <7, –2> and
v = <–1, 2>
As we know,
The angle between two vectors can be found using the below formula:
cosθ = (a.b)/|a| |b|
θ represents the angle between the vector a and b.
a is the first vector
b is the second vector
cosθ = [(7)(-1) + (-2)(2)]/(√7²+(-2)²)(√-1²+2²)
cosθ = [-11]/[(√53)(√5)]
cosθ = -11/(√265)
cosθ = -0.675
The trigonometric ratio is defined as the ratio of the pair of a right-angled triangle.
θ = 132.51 degrees
Thus, the angle between the two vectors u = <7, –2> and v = <–1, 2>. is 132.51 degrees.
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