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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