The distance between the point \((3,4,5)\) and the point where the line \(\frac{x-3}{1} = \frac{y-4}{2} = \frac{z-5}{2}\) meets the plane \(x+y+z=17\) is

The point of intersection of the lines \(\frac{x-1}{2} = \frac{y-2}{3} = \frac{z-3}{4}\) and \(\frac{x-4}{5} = \frac{y-1}{2} = z\) is

If events A and B are independent, then identify the correct statement (A) A and B must be mutually exclusive (B) The sum of their probabilities must be equal to 1 (C) \(P(A)\cdot P(B) = P(A\cap B)\) (D) \(A'\) and \(B'\) are also independent Choose the correct answer from the op…

If \(x(\hat{i}+\hat{j}+\hat{k})\) is a unit vector, then the value of \(x\) is:

The equation of the plane passing through the point \((0,7,-7)\) and containing the line \(\frac{x+1}{-3} = \frac{y-3}{2} = \frac{z+2}{1}\) is:

The area of the parallelogram whose adjacent sides are \(\hat{i}+\hat{k}\) and \(2\hat{i}+\hat{j}+\hat{k}\) is

If \(A\) and \(B\) are two independent events with \(P(A) = \frac{3}{5}\) and \(P(B) = \frac{4}{9}\), then \(P(A'\cap B')\) is equal to

The corner points of the feasible region for an L.P.P. are \((2,0)\), \((7,0)\), \((4,5)\) and \((0,3)\), and \(z = 2x+3y\) is the objective function. The difference of the maximum and minimum values of \(z\) is:

A line \(L: \frac{x-2}{1} = \frac{y-3}{2} = \frac{z-1}{-1}\) is perpendicular to a plane \(P\) which passes through the point \((4,3,9)\). If the mirror image of the point \(S\) on the line \(L\) in the plane \(P\) is \((2,3,1)\), then the co-ordinates of the point \(S\) are: