Respuesta :
Answer:
for all values
Step-by-step explanation:
u = (t - 2, 6 - t, - 4)
v = ( - 4, t - 2, 6 - t)
Angle between them, θ = 120°
Use the concept of dot product of two vectors
[tex]\overrightarrow{A}.\overrightarrow{B}=A B Cos\theta[/tex]
Magnitude of u = [tex]\sqrt{(t-2)^{2}+(6-t)^{2}+(-4)^{2}}[/tex]
= [tex]\sqrt{2t^{2}-16t+56}[/tex]
Magnitude of v = [tex]\sqrt{(t-2)^{2}+(6-t)^{2}+(-4)^{2}}[/tex]
= [tex]\sqrt{2t^{2}-16t+56}[/tex]
[tex]\overrightarrow{u}.\overrightarrow{v}=-4(t-2)+(6-t)(t-2)-4(6-t)=-t^{2}+8t-28[/tex]
By the formula of dot product of two vectors
[tex]Cos120 = \frac{-t^{2}+8t-28}{\sqrt{2t^{2}-16t+56}\times \sqrt{2t^{2}-16t+56}}[/tex]
[tex]-0.5\times {2t^{2}-16t+56} = {-t^{2}+8t-28}}[/tex]
[tex]{-t^{2}+8t-28}} = {-t^{2}+8t-28}}[/tex]
So, for all values of t the angle between these two vectors be 120.
