Question

Find the angle between two vectors a and b if a=i+2j+3k and b=2i-j

Answer 1

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Answer 2

Answer:

the angle between two vectors are 90°

Step-by-step explanation:

formula for angle between two vector is

cos∅ = a.b /|a| |b|

given, a = i + 2j + 3k , b = 2i - j

property of dot product

i.i = j.j = k.k = 1

i.j = j.k = k.i = 0

dot product of a & b is

a.b = (i + 2j + 3k).(2i - j)

a.b = 2 - 2 = 0

and

|a| = √(1² + 2² + 3²) = √14

|b| = √{2² + (-1)²} = √5

cos∅ = a.b/|a| |b|

cos∅ = 0/√14 √5

cos∅ = 0

cos∅ = cos90

∅ = 90°

thanks,

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