Two vectors, r and s lie in the xy pane. Their magnitudes are 3.15 and6.75 units

Question

Two vectors, r and s lie in the xy pane. Their magnitudes are 3.15 and6.75 units, respectively, and their directions are 3070 and 740, respectively, as measured counterdockwise from the positivexaxis What are the values of (a) r s and (b) r x s (a) Number Uni (b) Number nits A carisdriven east for a distanceof 47km, then north for 23km, and then in a diection 260 east of north for 28 km.Determine (a) the magnitude of the carstotaldisplacement from its starting point and (b) the angle (from east)ofthecarstotal dsplacement measured from its starting dredion. (a) Number (b) Number

Explanation / Answer

a)
r · s = |r| * |s| * cos()
where is angle between r and s.
= 307 -74 = 233o

r · s = 3.15 * 6.75 * cos(233o)
r · s = -12.8 units

b)
|r × s| = |r| |s| sin()
where is angle between r and s.
= 307 -74 = 233o
|r × s| = 3.15 * 6.75 * sin(233)
|r × s| = -16.98

Please post seperate question in seperate post.

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