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

Asked by RIZWAN YASIN | 15th Jun, 2013, 09:21: PM

Expert Answer:

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)

Answered by  | 15th Jun, 2013, 09:31: PM

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