+0

# Similar vector dot problem

+1
159
3
+223

this is the second answer i got

16.865987621884, is it correct. i cant afford to keep puttin in wrong answers. If its the answer then i know what im doing now.

Veteran  Mar 19, 2017
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#1
+223
0

here is another answer i got

156.161259816828

Veteran  Mar 19, 2017
#2
+76946
+5

u = < - 2, 8 >

v = < -7, - 9 >

cos (theta)   =   u (dot) v / [ ll u ll * ll v ll ]

u (dot) v   =   14 - 72  =   -58

ll u ll  =   sqrt [ (-2)^2 + (8)^2 ]  =  sqrt (68)

ll v ll   =   sqrt [ (-7)^2 + (-9)^2 ]   =  sqrt [ 49 + 81]   =  sqrt (130)

cos (theta)   =   -58 / [ sqrt (68) * sqrt (130) ]

arcos  [ -58 / [ sqrt (68) * sqrt (130) ] ]   = theta   ≈ 128.0888°

Here is a graph that shows this, Veteran :

CPhill  Mar 19, 2017
#3
+18612
0

rounded to at least four decimal places.

$$\vec{u} = \binom{-2}{8} \\ \vec{v} = \binom{-7}{-9} \\$$

$$\begin{array}{|rcll|} \hline \tan(\theta) &=& \frac{|~\vec{u} \times \vec{v}~| } {\vec{u} \cdot \vec{v} } \\ &=& \frac{ \left|~\binom{-2}{8} \times \binom{-7}{-9}~\right| } {\binom{-2}{8} \cdot \binom{-7}{-9} } \\ &=& \frac{ (-2)\cdot (-9) - (8)\cdot (-7) } { (-2)\cdot (-7) + (8)\cdot (-9) } \\ &=& \frac{ 18+56 } { 14-72 } \\ &=& \frac{ 74 } { -58 } \quad & | \quad II.\text{Quadrant} \\ &=& \frac{ 37 } { -29 } \\ \theta &=& \arctan(\frac{ 37 } { -29 }) \\ \theta &=& \arctan(-1.27586206897) \\ \theta &=& -51.9112271190180^{\circ} + 180^{\circ} \quad & | \quad II.\text{Quadrant} \\ \theta &=& 128.088772881^{\circ} \\ \theta &\approx& 128.0888^{\circ} \\ \hline \end{array}$$

heureka  Mar 20, 2017

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