if u-3v and mu+v are perpendicular determine the value of m.

[wine]

Unit vector u and v make an angle of 60 degree with each other. if u-3v and mu+v are perpendicular determine the value of m.
I only know that u-3v dot mu+v =0 and then i dont know how i can continue. Thank you.

 

[Ishuda]

Unit vector u and v make an angle of 60 degree with each other. if u-3v and mu+v are perpendicular determine the value of m.
I only know that u-3v dot mu+v =0 and then i dont know how i can continue. Thank you.

Ley u=(u₁, u₂, u₃) and similarly for v. Write out the dot product of u-3v and mu+v and use the fact that u and v are unit vectors and their dot product is \(\displaystyle \alpha\, =\, cos(\frac{\pi}{3})\) to simplify the equation.

 

[pka]

Unit vector u and v make an angle of 60 degree with each other. if u-3v and mu+v are perpendicular determine the value of m.
I only know that u-3v dot mu+v =0 and then i dont know how i can continue.

Come on, let's be grownup about this, use numbers: \(\displaystyle u \cdot v = \cos \left( {\frac{\pi }{3}} \right) = \frac{1}{2}\).
\(\displaystyle \left(\vec{u}-3\vec{v}\right)\cdot \left(m\vec{u}+\vec{v}\right)=m\left(\vec{u} \cdot \vec{u}\right)+\left(\vec{u}\cdot \vec{v}\right)-3m\left(\vec{u}\cdot\vec{v}\right)-3\left(\vec{v}\cdot\vec{v}\right)=~?\)

RECALL that \(\displaystyle \left(\vec{u}\cdot\vec{u}\right)=1\) WHY?

 

[pka]

Double Post