During maneuvers preceding the Battle of Jutland, the British battle cruiser Lion moved as follows (in nautical miles): 1.2 miles north, 6.1 miles 38 degrees east of south, 4.0 miles at 89 degrees east of north, and 6.5 miles at 31 degrees east of north. Find the distance between starting and ending positions. (Ignore the earth’s curvature.)

total distance is 11.3 miles

Explanation:

Given data:

distance to north = 1.2 miles

distance to south at 38 degree east of south = 6.1 miles  

distance to east of north at angle 89 degree = 4 miles  

distance to east of north at angle 31 degree =  6.5 miles

considering each displacement as vector so we have

total distance is

no. dot product   =0 when vecs at right angles

luster is not a good characteristic to use by itself because luster is the property of minerals that indicates how much the surface of a mineral reflects light. the luster of a mineral is affected by the brilliance of the light used to observe the mineral surface.