Three-dimension...

Equation of a plane parallel to xz plane at unit distance is 

What are the d.c's of the line whose d.r's are 1. -2. and 3 ?

What is the equation to the straight line passing through (a, b, c) and parallel to z-axis?

The value of k such that the line \(\frac{x-4}{1}=\frac{y-2}{1}=\frac{z-k}{2}\) is lying on the plane 2x - 4y + z  = 7 will be?

XY-plane divides the line joining the points A(2, 3, -5) and B(-1, -2, -3) in the ratio

Find distance between the lines L₁ and L₂ whose vector equations are \(\vec r = \;\hat i + \hat j + \hat k + \;\lambda \times \left( {3\hat i - \hat j} \right)\;and\;\vec r = 4\hat i-\hat k + \mu \times \left( {3\hat i - \hat j} \right)\)

Find the angle between the line \(\frac{{x + 1}}{2} = \frac{{y}}{{\;3}} = \frac{{z - 3}}{6}\) and the plane 10x + 2y - 11z - 3 = 0.

The locus of a point P(x, y, z) which moves in such a way that z = 7 is a

What are the direction ratios of the line of intersection of the planes x = 3z + 4 and y = 2z - 3?

If the lines \(\vec r = \overrightarrow {{a_1}} + \lambda \overrightarrow {{b_1}} \;and\;\vec r = \overrightarrow {{a_2}} + \mu \overrightarrow {{b_2}} \) are coplanar then which of the following is correct ?