Answer to Question #178939 in Calculus for John withers

Question #178939

Determine the angle between the following two vectors.

|𝑔| = (1,2,−3)


|h| = (0,−3,4)


1
Expert's answer
2021-04-29T18:06:56-0400

Let θ\theta be the angle between the vectors g\vec{g} and h\vec{h} .

Using the transformed dot product equation,


θ=cos1(ghgh)\theta = \cos^{-1} \left( \frac{ \vec{g}\cdot \vec{h}}{|\vec{g}| |\vec{h}| } \right)

where

gh=(1)(0)+(2)(3)+(3)(4)=18\vec{g}\cdot \vec{h} = (1)(0) + (2)(-3)+(-3)(4)=-18 (the dot product of g\vec{g} and h\vec{h} )

and

g=(1)2+(2)2+(3)2=14|\vec{g}| = \sqrt{(1)^2+(2)^2+(-3)^2} = \sqrt{14} (magnitude of vector g\vec{g} )

h=(0)2+(3)2+(4)2=25=5|\vec{h}| = \sqrt{(0)^2+(-3)^2+(4)^2} = \sqrt{25}=5 (magnitude of vector h\vec{h} )


Therefore,


θ=cos1(1814(5))\theta = \cos^{-1} \left( \frac{-18}{\sqrt{14} (5)} \right)

θ=cos1(0.9621)\theta = \cos^{-1} \left( -0.9621 \right)

θ=164.180\theta = 164.18^{0}


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment