The locus of the point, which moves such that its distance from (1, - 2, 2) is unity, will be

• x² + y² + z² - 2x + 4y - 4z + 8 = 0

• x² + y² + z² - 2x - 4y - 4z + 8 = 0

• x² + y² + z² + 2x + 4y - 4z + 8 = 0

• x² + y² + z² - 2x + 4y + 4z + 8 = 0

112.

The ratio in which the sphere x² + y² + z² = 504 divides the line segment AB joining the points A(12, - 4, 8) and B(27, - 9, 18) is given by

• 2 : 3 externally

• 2 : 3 internally

• 1 : 2 externally

• None of these

If the points (k, 2 - 2k), (- k + 1, 2k) and (- 4 - k, 6 - 2) are collinear, then k is equal to

• - 1

• $\frac{1}{3}$

• 1

• $- \frac{1}{2}$

The value of the angle between two straight lines y = $\left(2 - \sqrt{3}\right)\mathrm{x} + 5$ and $\mathrm{y} = \left(2 + \sqrt{3}\right)\mathrm{x} - 7$ is

• $30°$

• $60°$

• $45°$

• $90°$

If Z₁ = 1 + i, Z₂ = - 2 + 3i and Z₃ = $\frac{\mathrm{ai}}{3}$ are  collinear, where i² = - 1, then the value of a will be

• - 1

• 3

• 4

• 5

If one of the lines of pair of straight lines ax² + 2hxy + by²  = 0 bisects the angle between the coordinate axes, then

• a² + b² = h²

• (a + b)² = 4h²

• a² + b² = 4h²

• (a + b)² = h²

If the slope of one lne is twice the slope of other in the pair of straight lines ax² + 2hxy + by² = 0, then 8h² is equal to

• - 9ab

• 9ab

• - 7ab

• 7ab

If the extremities of diagonal of a square (1, - 2, 3), (2, - 3, 5), then the length of its side, is

• $\sqrt{6}$

• $\sqrt{3}$

• $\sqrt{5}$

• $\sqrt{7}$

The foot of the perpendicular from (0, 2, 3) to the line $\frac{\mathrm{x} + 3}{5} = \frac{\mathrm{y} - 1}{2} = \frac{\mathrm{z} +\hspace{0.17em}4}{3}$ is

• (- 2, 3, 4)

• (2, - 1, 3)

• (2, 3, - 1)

• (3, 2, - 1)

If a line makes angle $\frac{\mathrm{\pi }}{3} \mathrm{and} \frac{\mathrm{\pi }}{4}$ with the X-axis and Y-axis respectively, then the angle made by the line with the Z-axis is

• $\frac{\mathrm{\pi }}{2}$

• $\frac{\mathrm{\pi }}{4}$

• $\frac{5\mathrm{\pi }}{12}$

• $\frac{\mathrm{\pi }}{3}$