Find the angle between vectors u and v if u= i + 4j and v= -i+2j. a. 40.60 degrees b. 41.56 degrees c. 39.36 degrees d. 42.01 degrees e. 38.67 degrees
+118659
Find the angle between vectors u and v if u= i + 4j and v= -i+2j. a. 40.60 degrees b. 41.56 degrees c. 39.36 degrees d. 42.01 degrees e. 38.67 degrees
u is in the first quadrant. Angle with pos x axis is atan(4/1)
v is in the second quadrant Angle with pos x axis = 180-atan(2)
angle between them = 180-atan(2)-atan(4)
180-atan(2)-atan(4) = 40.601294645004 40.60 degrees
However I do not understand why there is an i and a j.
+129841 We can find the angle thusly :
cos θ = [ u (dot) v ] / [ ll u ll * ll v ll ]
u (dot) v = 1*-1 + 4 * 2 = 7
ll u ll = √[ 1*2 + 4^2 ] = √17
ll v ll = √ [(-1)^2 + 2^2] = √5
So ll u ll * ll v ll = √[17 * 5 ] = √85
So
cos θ = 7 / √85 and we can find θ using the cosine inverse
arccos [ 7 / √85 ] = θ = 40.6°
