Vector A+Vector B=2i and Vector A-Vector B=4j, then angle between VecA and VecB is:

Let vector a = ax i + ay j 

vector b = bx i + by j 

 

Hence, a+b = 2i 

 ax i + ay j  + bx i + by j  = 2i 

Hence, ax+ bx = 2; but ay + by = 0 i.e ay = -by (1)

 

Also, a-b = 4j

ax i + ay j  - bx i - by j  = 4j

Hence ax-bx = 0; and ay - by = 4

So, ax = bx and ay -by = 4  (2)

 

Solving equations 1 and 2

ax = bx = 1; ay = 2; by = -2

 

Hence a = i + 2j 

b = i -2j 

 

Using the dot product to compute the angle between vector a and b 

a.b = |a||b| cos(theta)

1-4 - sqrt(5) sqrt(5) cos(theta)

-3/5 = cos(theta) 

Hence, theta = cos^-1(-3/5)

So, the angle between the 2 vectors = cos^-1(-3/5)