Vector magnitude and direction

• magnifik
In summary, the question is asking for the magnitude and angle of the resultant force when two vectors, one in quadrant one and one in quadrant four, are added together. The correct magnitude of the resultant force is 28.66 N. However, there is discrepancy in the angle, with the correct answer likely falling between 12.37 degrees and 75 degrees.
magnifik

Homework Statement

Find the magnitude of the resultant force and the angle it makes with the positive x-axis

draw one vector from origin (0,0) in quadrant one that is 45 degrees (this is 20 lbs)

draw another vector from the origin (0,0) in quadrant four that is 30 degrees (this is 16 lbs)

The Attempt at a Solution

here's what i did initially
20cos(45)i + 20sin(45)j = 10*sqrt(2)i + 10*sqrt(2)j
16cos(-30)i + 16sin(-30)j = 8*sqrt(3)i - 8j
F = (10*sqrt(2)i + 10*sqrt(2)j) + (8*sqrt(3)i - 8j)
|F| = sqrt((10*sqrt(2)i + 10*sqrt(2)j)^2) + (8*sqrt(3)i - 8j)^2)) = 28.66 N
$$\vartheta$$ = (10*sqrt(2) - 8)/(10*sqrt(2) + 8*sqrt(3)) = 12.37 deg

but if you use cosine rule or sine rule, you get different answers...
The angle is 45* + 30* = 75*

Now we use the Cosine rule to find the magnitude of the resultant vector. The resultant vector is 22.1 lbs.

Use the Sin rule and the angle is 90.7* (basically 90*)

which one is right?

The angle of the resultant vector should be between the angles of your initial vectors. Your answer of 12.37 degrees seems reasonable...however, 75 degrees and 90.7 degrees do not.

What is vector magnitude?

Vector magnitude is the length or size of a vector. It is determined by the Pythagorean theorem, which states that the magnitude of a vector is equal to the square root of the sum of the squares of its components.

How is vector magnitude represented?

Vector magnitude is typically represented by a scalar, which is a single numerical value. This value can be positive or negative, depending on the direction of the vector.

What is vector direction?

Vector direction refers to the orientation or angle of a vector with respect to a reference point or axis. It is usually measured in degrees or radians.

How is vector direction represented?

Vector direction is typically represented by an arrow pointing in the direction of the vector. The angle of the arrow with respect to a reference axis indicates the direction of the vector.

How do you calculate the components of a vector from its magnitude and direction?

The x and y components of a vector can be calculated using trigonometric functions. The x component is equal to the vector magnitude multiplied by the cosine of the angle, and the y component is equal to the vector magnitude multiplied by the sine of the angle.

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