coneheadrachie coneheadrachie
  • 02-02-2017
  • Mathematics
contestada

Determine whether the vectors u and v are parallel, orthogonal, or neither.

u = <10, 6>, v = <9, 5>

Respuesta :

LammettHash
LammettHash LammettHash
  • 03-02-2017
[tex]\mathbf u\cdot\mathbf v=\|\mathbf u\|\|\mathbf v\|\cos\theta[/tex]

where [tex]\theta[/tex] is the angle between the vectors. You have

[tex]10\times9+6\times5=\sqrt{10^2+6^2}\sqrt{9^2+5^2}\cos\theta\iff \cos\theta=\dfrac{30}{\sqrt{901}}\implies \theta\approx1.909^\circ[/tex]

The vectors would be orthogonal if the dot product had been zero, but that's clearly not the case.

They would be parallel if the angle turned out to be [tex]0^\circ[/tex] or [tex]180^\circ[/tex], but that's also not the case.

So the answer is neither.
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