Three Dimensional Geometry · Mathematics · NDA

If (1, −1, 2) and (2, 1, −1) are the end points of a diameter of a sphere $x^2 + y^2 + z^2 + 2ux + 2vy + 2wz − 1 = 0$, then what is $u + v + w$ equal ...

If $\langle l, m, n \rangle$ are the direction cosines of a normal to the plane $2x − 3y + 6z + 4 = 0$, then what is the value of $49(7l^2 + m^2 − n^2...

A line through $(1, −1, 2)$ with direction ratios $\langle 3, 2, 2 \rangle$ meets the plane $x + 2y + 3z = 18$. What is the point of intersection of l...

If $p$ is the perpendicular distance from origin to the plane passing through $(1, 0, 0)$, $(0, 1, 0)$ and $(0, 0, 1)$, then what is $3p^2$ equal to?...

If L is the line with direction ratios < 3, -2, 6 > and passing through (1, -1, 1), then what are the coordinates of the points o...

Which one of the planes is parallel to the line $\rm \frac{x-2}{3}=\frac{y-3}{4}=\frac{z-4}{5}$ ?

What is the angle between the lines 2x = 3y = -z and 6x = -y = -4z?

What is the equation of the sphere concentric with the sphere x2 + y2 + z2 - 2x - 6y -8z - 5 = ...

A point P lies on the line joining A(1, 2, 3) and B(2, 10, 1). If z-coordinate of P is 7, what is the sum of other two coordinates? 

What is u + v + w equal to ? 

P(x, y, z) is any point on the sphere, then what is PA2 + PB2 equal to ?  

What is the value of k? 

What are the direction ratios of a line which is perpendicular to both the lines ?

Consider the points A(2, 4, 6), B(−2, −4, −2), C(4, 6, 4), and D(8, 14, 12). Which of the following statements is/are correct? 1. The points are the ...

Consider the equation of a sphere x2 + y2 + z2 − 4x − 6y − 8z − 16 = 0. Which of the following statements is/are correct ? 1. z-axis ...

A plane cuts intercepts 2, 2, 1 on the coordinate axes. What are the direction cosines of the normal to the plane?

Consider the following statements : 1. The direction ratios of y-axis can be <0, 4, 0> 2. The direction ratios of a line perpendicular to z-ax...

What is the value of k?

If p is the perpendicular distance from the centre of the sphere to the plane, then which one of the following is correct ?

What is the equation of the line through the origin and the centre of the sphere ?

What are the direction ratios of the normal to the plane ?

If p, q and r are the intercepts made by the plane on the coordinate axes respectively, then what is (p + q + r) equal to ?