Question

a vector points 1280 units along the x-axis, and -847 units along the y-axis. Find the magnitude and direction of the vector

Answer 1

Answer:

1530 units, -33.5°

Explanation:

Given the x-component and the y-component, the magnitude can be found with Pythagorean theorem:

v² = vx² + vy²

And the direction can be found with trigonometry:

θ = atan(vy / vx)

Given that vx = 1280 and vy = -847:

v² = (1280)² + (-847)²

v ≈ 1530

θ = atan(-847 / 1280)

θ ≈ -33.5° or 146.5°

θ is in the fourth quadrant, so θ = -33.5°.

Answer 2

Answer:

The answer to your question is:  magnitude:  1534.9 units

direction: 326.5°

Explanation:

Data

x = 1280 u

y = -847 y

Then as x is positive and y is negative this vector is quadrangle

To find the magnitude, we use the pythagorean theorem

c2 = a2 + b2

c2 = 1280² + (-847)² = 1638400 + 717409 = 2355809

c = 1534.9 units

to find the direction we use the tangent function

tanФ = os/as = -847/1280 = -0.661

Ф = 33.49

But it is in the 4th quadrangle, then

Ф = 360 - 33-49 = 326.5°