If vectors a =3 i +2 j +λ k and b =2 i -4 j +5 k, represent the two strips of the Red Cross sign placed outside a doctor's clinic, then the value of…

If vectors $\displaystyle \overrightarrow{\mathrm{a}}=3 \hat{\mathrm{i}}+2 \hat{\mathrm{j}}+\lambda \hat{\mathrm{k}}$ and $\displaystyle \overrightarrow{\mathrm{b}}=2 \hat{\mathrm{i}}-4 \hat{\mathrm{j}}+5 \hat{\mathrm{k}}$, represent the two strips of the Red Cross sign placed outside a doctor's clinic, then the value of $\displaystyle \lambda$ is :