Mathematics: 1/2x + 1/3y = 5 1/4x + y = 10

1/2x + 1/3y = 5 1/4x + y = 10 - id1213514109805056, SoccerHalo

alejandra216

05.01.2020

The angle between the two vectors given is of 146 degrees.

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Suppose there are two vectors, a and b.The angle between them is $\theta$ , given by the following expression:

$\cos{\theta} = \frac{u.v}{|u||v|}$

In which

u.v is the dot product between them.|u| and |v| are their norms.

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The vectors are: a = (1,-4,1), b = (0, 3, -3)

The dot product is: $ab = (1, -4, 1).(0, 3, -3) = 1\times0 -4\times3 + 1\times(-3) = -15$ The norms are:

$|u| = \sqrt{1^2 + (-4)^2 + 1^2} = \sqrt{18} = \sqrt{2 \times 9} = \sqrt{2}\sqrt{9} = 3\sqrt{2}$

$|v| = \sqrt{0^2 + 3^2 + (-3)^2} = \sqrt{18} = 3\sqrt{2}$

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Finding the angle:

$\cos{\theta} = \frac{u.v}{|u||v|}$

$\cos{\theta} = \frac{-15}{(3\sqrt{2})^2}$

$\cos{\theta} = -\frac{15}{18}$

$\cos{\theta} = -\frac{5}{6}$

$\theta = \cos^{-1}{(-\frac{5}{6})}$ }

Using a calculator:

$\theta = 146$

The angle between the two vectors is of 146 degrees.

A similar problem is given at link

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