What is the angle between the vectors 4i + 6j + 8k and 19i + 2j + 16k

Expert Answers

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The angle between two vectors A = a1*i + b1*j + c1*k and B = a2*i + b2*j + c2*k can be determined by using the fact that the dot product of two vectors A and B is defined as A`.`B = a1*a2 + b1*b2 + c1*c2 = |a||b|cos A, where A is the angle between the vectors.

Here A = 4i + 6j + 8k and B = 19i + 2j + 16k

A`.`B = 4*19 + 6*2 + 8*16 = |A||B|cos A

=> 216 = sqrt(4^2 + 6^2 + 8^2)*sqrt(19^2 + 2^2 + 16^2)*cos A

=> 216 = sqrt 116*sqrt 621*cos A

=> cos A = 216/(sqrt 116*sqrt 621)

=> cos A = 0.8047

A = arc cos (0.8047)

=> 36.41 degrees

The angle between the two vectors is 36.41 degrees

Approved by eNotes Editorial Team
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