A watermelon has the following coordinates: x = -6.0 m, y = 4.0 m, and z = 0.0 m

Question

A watermelon has the following coordinates:

x = -6.0 m, y = 4.0 m, and z = 0.0 m

Find its position vector in terms of the vector's magnitude and orientation.

1.) Magnitude?

2.) Angle in degrees as measured counterclockwise from the x-axis

3.) Sketch the vector on a right-handed coordinate system. If the watermelon is moved to the x y z coordinates (4.0 m, 0.0 m, 0.0 m), what is its displacement in unit-vector notation? i-component?

4.) j-component?

5.) k-component?

6.) What is its displacement in terms of a magnitude?

7.) What is its displacement in terms of orientation?

Explanation / Answer

Position vector in units of 1m. is:
(- 6.0, 4.0, 0)

Its magnitude is:
sqrt(6^2 + 4^2)
= sqrt(36 + 16)
= sqrt(52) = 7.21 m

Its angle relative to the x-axis is a where:
tan(a) = - 4.0 / 6.0
a = 33.69 deg. = 146.31 degree with x axis

Its displacement is:
(4 - (-6), 0 - 4, 0 - 0)
= (10, - 4, 0).

i component = 10 m

j component = -4 m

k component = 0 m

The magnitude is:
sqrt(10^2 + 4^2)
= sqrt(116). = 10.77 m

Its angle relative to the x axis is a where:
tan(a) = - 4 / 10
= 21.8 deg.= 158.2 with +x

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