Respuesta :
Answer:
The value of q are 0.781,-1.281.
Step-by-step explanation:
Given : Two vectors [tex]A=i+j+kq[/tex] and [tex]B=iq-2j+2kq[/tex] are perpendicular to each other.
To find : The value of q ?
Solution :
When two vectors are perpendicular to each other then their dot product is zero.
i.e. [tex]\vec{A}\cdot \vec{B}=0[/tex]
Two vectors [tex]A=i+j+kq[/tex] and [tex]B=iq-2j+2kq[/tex]
[tex](i+j+kq)\cdot (iq-2j+2kq)=0[/tex]
[tex](1)(q)+(1)(-2)+(q)(2q)=0[/tex]
[tex]q-2+2q^2=0[/tex]
[tex]2q^2+q-2=0[/tex]
[tex]2q^2+q-2=0[/tex]
Using quadratic formula,
[tex]q=\frac{-1\pm\sqrt{1^2-4(2)(-2)}}{2(2)}[/tex]
[tex]q=\frac{-1\pm\sqrt{17}}{4}[/tex]
[tex]q=\frac{-1+\sqrt{17}}{4},\frac{-1-\sqrt{17}}{4}[/tex]
[tex]q=0.781,-1.281[/tex]
Therefore, The value of q are 0.781,-1.281.
