121367 If the length of the perpendicular drawn from the point \(P(a, 4,2), a>0\) on the line \(\frac{x+1}{2}=\frac{y-3}{3}=\frac{z-1}{-1}\) is \(2 \sqrt{6}\) units and \(Q\left(\alpha_1, \alpha_2\right.\), \(\alpha_3\) ) is the image of the point \(P\) in this line, then \(a+\sum_{i=1}^3 \alpha_i\) is equal to :
121369
Let the plane containing the line of intersection of the planes
\(P_1: x+(\lambda+4) y+z=1\) and
\(P_2: \mathbf{2 x}+\mathbf{y}+\mathrm{z}=\mathbf{2}\) pass through the points \((0,1\), \(0)\) and \((1,0,1)\). Then the distance of the point ( \(2 \lambda, \lambda,-\lambda)\) from the plane \(P 2\) is
121372 The plane \(2 x-y+z=4\) intersects the line segment joining the points \(A(a,-2,4)\) and \(B(2\), \(b,-3)\) at the point \(C\) in the ratio \(2: 1\) and the distance of point \(C\) from the origin is \(\sqrt{5}\). If ab \(\lt 0\) and \(P\) is the point \((a-b, b, 2 b-a)\) then \(C^2\) is equal to
121367 If the length of the perpendicular drawn from the point \(P(a, 4,2), a>0\) on the line \(\frac{x+1}{2}=\frac{y-3}{3}=\frac{z-1}{-1}\) is \(2 \sqrt{6}\) units and \(Q\left(\alpha_1, \alpha_2\right.\), \(\alpha_3\) ) is the image of the point \(P\) in this line, then \(a+\sum_{i=1}^3 \alpha_i\) is equal to :
121369
Let the plane containing the line of intersection of the planes
\(P_1: x+(\lambda+4) y+z=1\) and
\(P_2: \mathbf{2 x}+\mathbf{y}+\mathrm{z}=\mathbf{2}\) pass through the points \((0,1\), \(0)\) and \((1,0,1)\). Then the distance of the point ( \(2 \lambda, \lambda,-\lambda)\) from the plane \(P 2\) is
121372 The plane \(2 x-y+z=4\) intersects the line segment joining the points \(A(a,-2,4)\) and \(B(2\), \(b,-3)\) at the point \(C\) in the ratio \(2: 1\) and the distance of point \(C\) from the origin is \(\sqrt{5}\). If ab \(\lt 0\) and \(P\) is the point \((a-b, b, 2 b-a)\) then \(C^2\) is equal to
121367 If the length of the perpendicular drawn from the point \(P(a, 4,2), a>0\) on the line \(\frac{x+1}{2}=\frac{y-3}{3}=\frac{z-1}{-1}\) is \(2 \sqrt{6}\) units and \(Q\left(\alpha_1, \alpha_2\right.\), \(\alpha_3\) ) is the image of the point \(P\) in this line, then \(a+\sum_{i=1}^3 \alpha_i\) is equal to :
121369
Let the plane containing the line of intersection of the planes
\(P_1: x+(\lambda+4) y+z=1\) and
\(P_2: \mathbf{2 x}+\mathbf{y}+\mathrm{z}=\mathbf{2}\) pass through the points \((0,1\), \(0)\) and \((1,0,1)\). Then the distance of the point ( \(2 \lambda, \lambda,-\lambda)\) from the plane \(P 2\) is
121372 The plane \(2 x-y+z=4\) intersects the line segment joining the points \(A(a,-2,4)\) and \(B(2\), \(b,-3)\) at the point \(C\) in the ratio \(2: 1\) and the distance of point \(C\) from the origin is \(\sqrt{5}\). If ab \(\lt 0\) and \(P\) is the point \((a-b, b, 2 b-a)\) then \(C^2\) is equal to
121367 If the length of the perpendicular drawn from the point \(P(a, 4,2), a>0\) on the line \(\frac{x+1}{2}=\frac{y-3}{3}=\frac{z-1}{-1}\) is \(2 \sqrt{6}\) units and \(Q\left(\alpha_1, \alpha_2\right.\), \(\alpha_3\) ) is the image of the point \(P\) in this line, then \(a+\sum_{i=1}^3 \alpha_i\) is equal to :
121369
Let the plane containing the line of intersection of the planes
\(P_1: x+(\lambda+4) y+z=1\) and
\(P_2: \mathbf{2 x}+\mathbf{y}+\mathrm{z}=\mathbf{2}\) pass through the points \((0,1\), \(0)\) and \((1,0,1)\). Then the distance of the point ( \(2 \lambda, \lambda,-\lambda)\) from the plane \(P 2\) is
121372 The plane \(2 x-y+z=4\) intersects the line segment joining the points \(A(a,-2,4)\) and \(B(2\), \(b,-3)\) at the point \(C\) in the ratio \(2: 1\) and the distance of point \(C\) from the origin is \(\sqrt{5}\). If ab \(\lt 0\) and \(P\) is the point \((a-b, b, 2 b-a)\) then \(C^2\) is equal to