For what values of q are the two vectors A = i + j + kq each other and B-iq-23 + 2kg perpendicular to

Accepted Solution

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.