Let,\(\vec{a}=a\hat{i}+2\hat{j}−\hat{k}\) and \(\vec{b}=−2\hat{i}+α\hat{j}+\hat{k}\), where α ∈ R. If the area of the parallelogram whose adjacent sides are represented by the vectors \(\vec{a}\) and \(\vec{b}\) is \(\sqrt{15(α^2+4)}\) , then the value of \(2|\vec{a}|^2+(\vec{a}⋅\vec{b})|\vec{b}|^2 \)is equal to :
To a bird in air, a fish in water appears to be at 30 cm from the surface. If refractive index of water with respect to air is \(\frac {4}{3}\) ,the real distance of bird from the surface is
Let f(x) = [2x2 + 1] and \(g(x)=\left\{\begin{matrix} 2x-3,\,x<0&\\2x+3, x≥0 &\end{matrix}\right.\)where [t] is the greatest integer ≤ t. Then, in the open interval (–1, 1), the number of points where fog is discontinuous is equal to _______.
