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

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

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:

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 value of \(\hat{i}\cdot(\hat{j}\times\hat{k})+\hat{j}\cdot(\hat{i}\times\hat{k})+\hat{k}\cdot(\hat{i}\times\hat{j})\) 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