121424 A vector \(\overrightarrow{\mathbf{v}}\) in the first octant is inclined to the \(x\) - axis at \(60^{\circ}\), to the \(y\)-axis at \(45^{\circ}\) and to the \(z-\) axis at an acute angle. If a plane passing through the points \((\sqrt{2},-1,1)\) and (a, b, c) is normal to \(\overrightarrow{\mathbf{v}}\), then

121425 The length of the perpendicular drawn from
\((1,2,3)\) to the line \(\frac{x-6}{3}=\frac{y-7}{2}=\frac{x-7}{-2}\) is

121427 If the foot of the perpendicular drawn from (1, \(9,7)\) to the line passing through the point \((3,2\), 1) and parallel to the planes \(x+2 y+z=0\) and \(3 y-z=3\) is \((\alpha, \beta, \gamma)\), the \(\alpha+\beta+\gamma\) is equal to

121430 If the lengths of projections of a line of length ' \(l\) ' over the co-ordinate axes are \(l_1, l_2\) and \(l_3\) respectively, then \(l_1^2+l_2^2+l_3^2=\)

121424 A vector \(\overrightarrow{\mathbf{v}}\) in the first octant is inclined to the \(x\) - axis at \(60^{\circ}\), to the \(y\)-axis at \(45^{\circ}\) and to the \(z-\) axis at an acute angle. If a plane passing through the points \((\sqrt{2},-1,1)\) and (a, b, c) is normal to \(\overrightarrow{\mathbf{v}}\), then

121425 The length of the perpendicular drawn from
\((1,2,3)\) to the line \(\frac{x-6}{3}=\frac{y-7}{2}=\frac{x-7}{-2}\) is

121427 If the foot of the perpendicular drawn from (1, \(9,7)\) to the line passing through the point \((3,2\), 1) and parallel to the planes \(x+2 y+z=0\) and \(3 y-z=3\) is \((\alpha, \beta, \gamma)\), the \(\alpha+\beta+\gamma\) is equal to

121430 If the lengths of projections of a line of length ' \(l\) ' over the co-ordinate axes are \(l_1, l_2\) and \(l_3\) respectively, then \(l_1^2+l_2^2+l_3^2=\)

121424 A vector \(\overrightarrow{\mathbf{v}}\) in the first octant is inclined to the \(x\) - axis at \(60^{\circ}\), to the \(y\)-axis at \(45^{\circ}\) and to the \(z-\) axis at an acute angle. If a plane passing through the points \((\sqrt{2},-1,1)\) and (a, b, c) is normal to \(\overrightarrow{\mathbf{v}}\), then

121425 The length of the perpendicular drawn from
\((1,2,3)\) to the line \(\frac{x-6}{3}=\frac{y-7}{2}=\frac{x-7}{-2}\) is

121427 If the foot of the perpendicular drawn from (1, \(9,7)\) to the line passing through the point \((3,2\), 1) and parallel to the planes \(x+2 y+z=0\) and \(3 y-z=3\) is \((\alpha, \beta, \gamma)\), the \(\alpha+\beta+\gamma\) is equal to

121430 If the lengths of projections of a line of length ' \(l\) ' over the co-ordinate axes are \(l_1, l_2\) and \(l_3\) respectively, then \(l_1^2+l_2^2+l_3^2=\)

121424 A vector \(\overrightarrow{\mathbf{v}}\) in the first octant is inclined to the \(x\) - axis at \(60^{\circ}\), to the \(y\)-axis at \(45^{\circ}\) and to the \(z-\) axis at an acute angle. If a plane passing through the points \((\sqrt{2},-1,1)\) and (a, b, c) is normal to \(\overrightarrow{\mathbf{v}}\), then

121425 The length of the perpendicular drawn from
\((1,2,3)\) to the line \(\frac{x-6}{3}=\frac{y-7}{2}=\frac{x-7}{-2}\) is

121427 If the foot of the perpendicular drawn from (1, \(9,7)\) to the line passing through the point \((3,2\), 1) and parallel to the planes \(x+2 y+z=0\) and \(3 y-z=3\) is \((\alpha, \beta, \gamma)\), the \(\alpha+\beta+\gamma\) is equal to

121430 If the lengths of projections of a line of length ' \(l\) ' over the co-ordinate axes are \(l_1, l_2\) and \(l_3\) respectively, then \(l_1^2+l_2^2+l_3^2=\)