The equation of the plane which is equidistant from the two parallel planes 2x - 2y + z + 3= 0 and 4x - 4y + 2z + 9 = 0 is

• 8x - 8y + 4z + 15 = 0

• 8x - 8y + 4z - 15 = 0

• 8x - 8y + 4z + 3 = 0

• 8x - 8y + 4z - 3 = 0

The angle between the planes 3x + 4y + 5z = 3 and 4x - 3y + 5z = 9 is equal to

• $\frac{\mathrm{\pi }}{2}$

• $\frac{\mathrm{\pi }}{4}$

• $\frac{\mathrm{\pi }}{6}$

• $\frac{\mathrm{\pi }}{3}$

The vector equation of the plane through the point (2, 1, - 1) and parallel to the plane r - (i + 3j - k) = 0 is

• r . (i + 9j + 11k) = 6

• r . (i - 9j + 11k) = 4

• r . (i + 3j - k) = 6

• r . (i + 3j - k) = 4

If the foot of the perpendicular drawn from the point (5, 1, - 3) to a plane is (1, - 1, 3), then the equation of the plane is

• 2x + y - 3z + 8 = 0

• 2x + y + 3z + 8 = 0

• 2x - y - 3z + 8 = 0

• 2x - y + 3z + 8 = 0

The equation of the plane through the line of intersection of the planes x - y + z + 3 = 0 and x + y + 22 + 1 = 0 and parallel to x-axis is

• 2y - z = 2

• 2y + z = 2

• 4y + z = 4

• y - 2z = 3

If 3p + 2q = i + j + k and 3p - 2q = i - j - k, then the angle between p and q is

• $\frac{\mathrm{\pi }}{6}$

• $\frac{\mathrm{\pi }}{4}$

• $\frac{\mathrm{\pi }}{3}$

• $\frac{\mathrm{\pi }}{2}$

   

The point of intersection of the straight line $\frac{\mathrm{x} - 2}{2} = \frac{\mathrm{y} - 1}{- 3} = \frac{\mathrm{z} + 2}{1}$ with the plane x + 3y - z + 1 = 0 is

• (3, - 1, 1)

• (- 5, 1, - 1)

• (2, 0, 3)

• (4, - 2, - 1)

478.

If the lines $\frac{2\mathrm{x} - 1}{2} = \frac{3 - \mathrm{y}}{1} = \frac{\mathrm{z} - 1}{3}$ and $\frac{\mathrm{x} + 3}{2} = \frac{\mathrm{z} + 1}{\mathrm{p}} = \frac{\mathrm{y} + 2}{5}$ are perpendicular to each other, then p is equal to

• 1

• - 1

• 10

• - $\frac{7}{5}$

The point P(x, y, z) lies in the first octant and its distance from the origin is 12 units. If the position vector of P make 45° and 60° with the x-axis and y-axis respectively, then the coordinates of P are

• $\left(3\sqrt{3}, 6, 3\sqrt{2}\right)$

• $\left(4\sqrt{3}, 8, 4\sqrt{2}\right)$

• $\left(6\sqrt{2}, 6, 6\right)$

• $\left(6, 6, 6\sqrt{2}\right)$

The distance between the planes r . (i + 2j - 2k) + 5 = 0 and r . (2i + 4j - 4k) - 16 = 0 is

• 3

• $\frac{11}{3}$

• 13

• $\frac{13}{3}$