Vector a is expressed in magnitude and direction form as a⃗ =⟨√26,140∘⟩ .
What is the component form a⃗ ?
The component form of vector a⃗ can be found by using the magnitude and direction given. In this case, the magnitude is √26 and the direction is 140 degrees.
To find the x-component, we use the formula cos(θ) = x/√26, where θ is the direction. Solving for x, we get x = cos(140) * √26.
To find the y-component, we use the formula sin(θ) = y/√26, where θ is the direction. Solving for y, we get y = sin(140) * √26.
So the component form of a⃗ is a⃗ = ⟨cos(140) * √26, sin(140) * √26⟩.
To find the component form of vector a⃗, we can use the following steps:
1. Start by resolving the magnitude and direction of the vector into its horizontal and vertical components.
- The magnitude of vector a⃗ is given as √26.
- The direction of vector a⃗ is given as 140∘.
2. Convert the direction of vector a⃗ from degrees to radians.
- 1 degree = π/180 radians.
- 140∘ = 140 * π/180 radians.
3. Calculate the horizontal and vertical components of vector a⃗ using trigonometry.
- The horizontal component, aₓ, can be found by multiplying the magnitude by the cosine of the direction: aₓ = √26 * cos(140π/180).
- The vertical component, aᵧ, can be found by multiplying the magnitude by the sine of the direction: aᵧ = √26 * sin(140π/180).
Therefore, the component form of vector a⃗ is a⃗ = ⟨aₓ, aᵧ⟩, where aₓ is the horizontal component and aᵧ is the vertical component.
To find the component form of vector a, we need to convert it from magnitude and direction form to its X and Y components.
In magnitude and direction form, ⟨√26,140∘⟩, the magnitude of the vector is represented by √26, which is the length of the vector, and the direction is represented by 140 degrees.
To convert this into component form, we can use trigonometry. The X component of the vector, a⃗x, is given by:
a⃗x = magnitude × cos(direction)
In this case, the magnitude is √26, so a⃗x = √26 × cos(140∘).
Similarly, the Y component of the vector, a⃗y, is given by:
a⃗y = magnitude × sin(direction)
In this case, the magnitude is √26, so a⃗y = √26 × sin(140∘).
Therefore, the component form of vector a⃗ is a⃗ = ⟨√26 × cos(140∘), √26 × sin(140∘)⟩.
x = r cosθ
y = r sinθ
so just plug in your numbers