Find the component form of v given its magnitude and the angle it makes with the positive x-axis.
Magnitude of v= 2
Angle= v in the direction i+3j
so the direction vector is
(i+3j)/sqrt10
The i component of
2@directionabove= 2/sqrt10
and the y component is
1*3/sqrt10
Thanks!
I have a question: Is the length of a vector the same thing as its magnitude?
yes
and I see I have a typo on the y component
y component= 2*3/sqrt10
To find the component form of vector v given its magnitude and the angle it makes with the positive x-axis, follow these steps:
Step 1: Express the angle in terms of its trigonometric functions.
In this case, the angle "v" can be expressed as arctan(3/1) since it is in the direction of i + 3j. This simplifies to arctan(3).
Step 2: Convert the angle to radians.
Most calculators and programming languages use radians for trigonometric functions, so it's important to convert angles to radians if necessary. Since the given angle is in degrees, convert it to radians by multiplying it by π/180. Thus, the angle is arctan(3) * π/180.
Step 3: Use the trigonometric functions to find the x and y components.
The x-component can be found by multiplying the magnitude of v by the cosine of the angle, and the y-component can be found by multiplying the magnitude of v by the sine of the angle.
x-component = 2 * cos(arctan(3) * π/180)
y-component = 2 * sin(arctan(3) * π/180)
Step 4: Simplify the expressions and write the component form.
Using a calculator or programming language, compute the values for the x and y components.
x-component ≈ 0.2743
y-component ≈ 1.8226
Therefore, the component form of vector v is (0.2743, 1.8226).