What is the angle between #<9,7,1># and #<8,3,6> #?

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Answer 1 · 2016-03-02T13:05:49

#alpha ~~34.06^@#

The angle #alpha# between the two vectors

#vec u = < 9,7,1># and #vec v = <8,3,6>#

can be computed with the formula

#cos alpha = (vec u * vec v ) / (|| vec u || * || vec v ||)#

where the product in the numerator is a dot product.

In your case, this means:

# cos alpha = (9 * 8 + 7 * 3 + 1 * 6) / (sqrt(9^2 + 7^2 + 1^2) * sqrt(8^2 + 3^2 + 6^2)) = (99)/(sqrt(131)*sqrt(109)) ~~ 0.8285#

Thus,

#alpha ~~34.06^@#