treslagosnv

2022-01-21

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

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.$\mathrm{cos}\theta =\frac{A\cdot B}{\left|\left|A\right|\right|\cdot \left|\left|B\right|\right|}$

$\therefore \theta ={\mathrm{cos}}^{-1}\left(\frac{\begin{array}{c}(1,3,-8)\cdot (4,1,5)\end{array}}{\left||1,3,-8|\right|\cdot \left||4,1,5|\right|}\right)$

$={\mathrm{cos}}^{-1}\left(\frac{4+3-40}{\sqrt{72\sqrt{42}}}\right)$

$=126,{294}^{\circ}$

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.

An object moving in the xy-plane is acted on by a conservative force described by the potential energy function

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?Find a nonzero vector orthogonal to the plane through the points P, Q, and R. and area of the triangle PQR

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