Find angle between the vector vec(a) =<1,2,2> and vec(b)=<3,4,0> in nearest degree

MISA6zh

MISA6zh

Answered question

2022-11-09

Find angle between the vector a =< 1 , 2 , 2 > and b =< 3 , 4 , 0 > in nearest degree
What I try:
cos θ = a b | a | | b | = 3 + 8 3 × 5 = 11 25
I did not understand how can I convert it into degrees.

Answer & Explanation

Kailee Abbott

Kailee Abbott

Beginner2022-11-10Added 14 answers

We begin by finding the dot product of the two vectors.
a b = ( 1 ) ( 3 ) + ( 2 ) ( 4 ) + ( 2 ) ( 0 ) = 3 + 8 + 0 = 11
Next, let us find the magnitude of the first vector.
a = ( 1 ) 2 + ( 2 ) 2 + ( 2 ) 2 = 9 = 3
Now, the magnitude of the second vector.
b = ( 3 ) 2 + ( 4 ) 2 + ( 0 ) 2 = 25 = 5
We can now find the angle between these two vectors.
cos ( θ ) = 11 3 5 θ = arccos ( 11 15 ) 42.83 °
Thus, the angle measurement is approximately 43 degrees.

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