The equation of the plane passing through the point (1, 2, -3) and perpendicular to the planes 3x + y – 2z = 5 and

The distance of the point P(3,4,4) from the point of intersection of the line joining the points Q(3,-4,-5) and R(2,-3,1) and the plane 2x + y + z = 7, is equal to………..

For real numbers α and β ≠ 0, if the point of intersection of the straight lines (x-α)/1 = (y-1)/2 = (z-1)/3 and (x-4)/β = (y-6)/3 = (z-7)/3 lies on the plane x+2y-z = 8, then α - β is equal to:

Let f : [0,∞) → be a function defined by f(x) = { max{sint: 0≤ t ≤x}, 0≤x≤π, 2 + cos x, x > π
Then which of the following is true?
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The distance of the point (1, 1, 9) form the point of intersection of the line $\frac{x-3}{1}=\frac{y-4}{2}=\frac{z-5}{2}$ <!-- [if gte mso 9]><xml> </xml><![endif]--> and the plane  x + y + z = 17 is:

Let $\lambda$ <!-- [if gte mso 9]><xml> </xml><![endif]--> be an integer. IF the shortest distance between the lines $x-\lambda =2y-1=-2z$ <!-- [if gte mso 9]><xml> </xml><![endif]--> and $x=y+2\lambda =z-\lambda is\frac{\sqrt[]{7}}{2\sqrt[]{2}}$ <!-- [if gte mso 9]><xml> </xml><![endif]-->, then the value of <!-- [if gte mso 9]><xml> </xml><![endif]-->  $\left|\lambda \right|is...................$