If P = (0, 1, 0), Q = (0, 1, 0), then the projection of PQ on the plane x + y + z = 3 is

• 2

• $\sqrt{2}$

• 3

• $\sqrt{3}$

In the space the equation by + cz + d = 0 represents a plane perpendicular to the

• YOZ-plane

• ZOX-plane

• XOY-plane

• None of these

A plane x passes through the point (1, 1, 1). If b, c, a are the direction ratios of a normal to the plane, where a, b, c (a < b < c) are the factors of 2001, then the equation of plane is 

• 29x + 31y + 3z = 63

• 23x + 29y - 29z = 23

• 23x + 29y + 3z = 55

• 31x + 37y + 3z = 71

If the plane 7x + 11y + 13z = 3003 meets the co-ordinate axes in A, B, C, then the centroid of the $∆\mathrm{ABC}$ is

• (143, 91, 77)

• (143, 77, 91)

• (91, 143, 77)

• (143, 66, 91)

If a,b, c are three non-coplanar vectors, then the vector equation $\overrightarrow{\mathrm{r}} = \left(1 - \mathrm{p} - \mathrm{q}\right)\overrightarrow{\mathrm{a}} + \mathrm{p}\overrightarrow{\mathrm{b}} + \mathrm{q}\overrightarrow{\mathrm{c}}$ represents a :

• straight line

• plane

• plane apssing through origin

• sphere

If a,b, c are three vectors such that $\overrightarrow{\mathrm{a}} = \overrightarrow{\mathrm{b}} + \overrightarrow{\mathrm{c}}$ and the angle between $\overrightarrow{\mathrm{b}} \mathrm{and} \overrightarrow{\mathrm{c}}$ is $\frac{\mathrm{\pi }}{2}$, then

• a² = b² + c²

• b² = c² + a²

• c² = a² + b²

• 2a² - b² = c²

XOZ-plane divides the join of (2, 3, 1) and(6, 7, 1) in the ratio :

• 3 : 7

• 2 : 7

• - 3 : 7

• - 2 : 7

If the direction ratio of two lines are given by 3lm - 4ln + mn = 0 and l + 2m + 3n = 0, then the angle between the lines, is :

• $\frac{\mathrm{\pi }}{6}$

• $\frac{\mathrm{\pi }}{4}$

• $\frac{\mathrm{\pi }}{3}$

• $\frac{\mathrm{\pi }}{2}$

A plane makes intercepts 3 and 4 respectively on Z-axis and X-axis. If it is parallel to Y-axis, then its equation is

• 3x + 4z = 12

• 3z + 4x = 12

• 3y + 4z = 12

• 3z + 4y = 12

The equation of the plane passing through(1, 1, 1) and   (1, - 1, - 1) and perpendicular to 2x -y + z = 0 is :

• 2x +5y +z + 8 = 0

• x + y - z - 1 = 0

• 2x + 5y + z + 4 = 0

• x - y + z - 1 = 0