The angle of a vector with the positive x-axis can be found using the formula for the tangent of the angle, which is the ratio of the y-component to the x-component.

In this case, we know the magnitude (r) of the vector is 10 units and the y-component (y) is 5 units.

We can use the Pythagorean theorem to find the x-component (x): r^2 = x^2 + y^2. Substituting the given values, we get 10^2 = x^2 + 5^2, which simplifies to 100 = x^2 + 25. Solving for x, we find x = sqrt(75) = 8.66 units.

Now we can find the angle. The tangent of the angle (θ) is y/x, so tan(θ) = 5/8.66.

Taking the inverse tangent of both sides to solve for θ, we get θ = arctan(5/8.66).

Using a calculator, we find that θ = 30 degrees.

So, the angle of the vector with the positive x-axis is 30 degrees.

Question

The angle of a vector with the positive x-axis can be found using the formula for the tangent of the angle, which is the ratio of the y-component to the x-component.

In this case, we know the magnitude (r) of the vector is 10 units and the y-component (y) is 5 units.

We can use the Pythagorean theorem to find the x-component (x): r^2 = x^2 + y^2. Substituting the given values, we get 10^2 = x^2 + 5^2, which simplifies to 100 = x^2 + 25. Solving for x, we find x = sqrt(75) = 8.66 units.

Now we can find the angle. The tangent of the angle (θ) is y/x, so tan(θ) = 5/8.66.

Taking the inverse tangent of both sides to solve for θ, we get θ = arctan(5/8.66).

Using a calculator, we find that θ = 30 degrees.

So, the angle of the vector with the positive x-axis is 30 degrees.

Knowee AI · Accepted Answer

The angle of a vector with the positive x-axis can be found using the formula for the tangent of the angle, which is the ratio of the y-component to the x-component.

In this case, we know the magnitude (r) of the vector is 10 units and the y-component (y) is 5 units.

We can use the Pythagorean theorem to find the x-component (x): r^2 = x^2 + y^2. Substituting the given values, we get 10^2 = x^2 + 5^2, which simplifies to 100 = x^2 + 25. Solving for x, we find x = sqrt(75) = 8.66 units.

Now we can find the angle. The tangent of the angle (θ) is y/x, so tan(θ) = 5/8.66.

Taking the inverse tangent of both sides to solve for θ, we get θ = arctan(5/8.66).

Using a calculator, we find that θ = 30 degrees.

So, the angle of the vector with the positive x-axis is 30 degrees.

A vector has a magnitude of 10 units and its y-component is 5 units. What is its angle with positive x-axis?Group of answer choices60o45o30o0.52o90o

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A vector has a magnitude of 10 units and its y-component is 5 units. What is its angle with positive x-axis?

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