Question

Vectors a and b have identical magnitudes of 7.5 units. find the angle between them if a + b = 7.5 3 ĵ. (enter the smallest positive angle in degrees.)

Answer 1

For this case you can find the module of the sum of the two vectors by means of the following equation
a + b = root (a^2 + b^2 + 2*a*b*cos (x)) --- Eq1
On the other hand the vector a + b is
a + b = 7.5*3 ĵ = 22.5 j
The module of a + b is
a + b = Root (22.5^2) = 22.5
Substituting values in Eq1
22.5 = root ((7.5)^2 + (7.5)^2 + 2*(7.5)*(7.5)*cos (x))
Clearing
x = arccos [((22.5^2) - (7.5)^2 - (7.5)^2)/(2*(7.5)*(7.5))]
x = ARCOS (3.5)
the angle between a and b in degrees is
x = ARCOS (3.5*(180/pi))