88407 \(\Pi_{1}, \Pi_{2}, \Pi_{3}\) are three planes which are respectively parallel to the \(Y Z, Z X\) and \(X Y\) planes at distances \(a, b\) and \(c\) forming \(a\) rectangular parallelepiped. \(d_{1}\) is a diagonal of the face of \(\mathrm{XY}\)-plane not passing through the origin and \(d_{2}\) is a diagonal of the plane \(\mathbf{I I}_{2}\) coterminous with \(d_{1}\). If none of the coordinates of the vertices of the parallelopiped are negative, then the angle between \(d_{1}\) and \(d_{2}\) is

88408 The acute angle between the pair of straight lines joining the origin to the points of intersection of the line \(x+y-1=0\) with the pair of straight lines
\(k x^{2}+8 x y-3 y^{2}+2 x-4 y-1=0\) is

88409 Angles made with the \(\mathrm{X}\)-axis by the two lines passing through the point \(P(1,2)\) and cutting the line \(x+y=4\) at a distance \(\frac{\sqrt{6}}{3}\) units from the point \(P\) are

88407 \(\Pi_{1}, \Pi_{2}, \Pi_{3}\) are three planes which are respectively parallel to the \(Y Z, Z X\) and \(X Y\) planes at distances \(a, b\) and \(c\) forming \(a\) rectangular parallelepiped. \(d_{1}\) is a diagonal of the face of \(\mathrm{XY}\)-plane not passing through the origin and \(d_{2}\) is a diagonal of the plane \(\mathbf{I I}_{2}\) coterminous with \(d_{1}\). If none of the coordinates of the vertices of the parallelopiped are negative, then the angle between \(d_{1}\) and \(d_{2}\) is

88408 The acute angle between the pair of straight lines joining the origin to the points of intersection of the line \(x+y-1=0\) with the pair of straight lines
\(k x^{2}+8 x y-3 y^{2}+2 x-4 y-1=0\) is

88409 Angles made with the \(\mathrm{X}\)-axis by the two lines passing through the point \(P(1,2)\) and cutting the line \(x+y=4\) at a distance \(\frac{\sqrt{6}}{3}\) units from the point \(P\) are

88407 \(\Pi_{1}, \Pi_{2}, \Pi_{3}\) are three planes which are respectively parallel to the \(Y Z, Z X\) and \(X Y\) planes at distances \(a, b\) and \(c\) forming \(a\) rectangular parallelepiped. \(d_{1}\) is a diagonal of the face of \(\mathrm{XY}\)-plane not passing through the origin and \(d_{2}\) is a diagonal of the plane \(\mathbf{I I}_{2}\) coterminous with \(d_{1}\). If none of the coordinates of the vertices of the parallelopiped are negative, then the angle between \(d_{1}\) and \(d_{2}\) is

88408 The acute angle between the pair of straight lines joining the origin to the points of intersection of the line \(x+y-1=0\) with the pair of straight lines
\(k x^{2}+8 x y-3 y^{2}+2 x-4 y-1=0\) is

88409 Angles made with the \(\mathrm{X}\)-axis by the two lines passing through the point \(P(1,2)\) and cutting the line \(x+y=4\) at a distance \(\frac{\sqrt{6}}{3}\) units from the point \(P\) are