treslagosnv

## Answered question

2022-01-21

What is the angle between <1,3,−8> and <4,1,5>

### Answer & Explanation

Madelyn Townsend

Beginner2022-01-22Added 13 answers

There are 2 methods we can use to calculate this algebraically, either using the vector cross product or the vector inner product.
The angle between any 2 vectors A and B in any dimensional vector space may be given by the inverse cosine of the Euclidean inner product of the 2 vectors divided by the product of the norms of the 2 vectors.
i.e. $\mathrm{cos}\theta =\frac{A\cdot B}{||A||\cdot ||B||}$
$\therefore \theta ={\mathrm{cos}}^{-1}\left(\frac{\begin{array}{c}\left(1,3,-8\right)\cdot \left(4,1,5\right)\end{array}}{||1,3,-8||\cdot ||4,1,5||}\right)$
$={\mathrm{cos}}^{-1}\left(\frac{4+3-40}{\sqrt{72\sqrt{42}}}\right)$
$=126,{294}^{\circ }$

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