2.2 Coordinate Systems and Components of a Vector

A blue fly lands on a sheet of graph paper at a point located 10.0 cm to the right of its left edge and 8.0 cm above its bottom edge and walks slowly to a point located 5.0 cm from the left edge and 5.0 cm from the bottom edge. Choose the rectangular coordinate system with the origin at the lower left-side corner of the paper and find the displacement vector of the fly. Illustrate your solution b…

If the displacement vector of a blue fly walking on a sheet of graph paper is $\overset{\rightarrow}{D} = \left(−5.00 \hat{i} - 3.00 \hat{j}\right) \text{cm}$, find its magnitude and direction.

If Trooper runs 20 m west before taking a rest, what is his displacement vector?

If the average velocity vector of the drone in the displacement in the example is $\overset{\rightarrow}{u} = \left(15.0 \hat{i} + 31.7 \hat{j} + 2.5 \hat{k}\right) \text{m} / \text{s}$, what is the magnitude of the drone’s velocity vector?

Give an example of a nonzero vector that has a component of zero.

If two vectors are equal, what can you say about their components?

If one of the two components of a vector is not zero, can the magnitude of the other vector component of this vector be zero?

You drive 7.50 km in a straight line in a direction $15 °$ east of north. (a) Find the distances you would have to drive straight east and then straight north to arrive at the same point. (b) Show that you still arrive at the same point if the east and north legs are reversed in order. Assume the +x-axis is to the east.

Two points in a plane have polar coordinates $P_{1} \left(2.500 \text{m} , \pi / 6\right)$ and $P_{2} \left(3.800 \text{m} , 2 \pi / 3\right)$. Determine their Cartesian coordinates and the distance between them in the Cartesian coordinate system. Round the distance to a nearest centimeter.

Two points in the Cartesian plane are A(2.00 m, −4.00 m) and B(−3.00 m, 3.00 m). Find the distance between them and their polar coordinates.