If the line $\frac{\mathrm{x} - 4}{1} = \frac{\mathrm{y} - 2}{1} = \frac{\mathrm{z} - \mathrm{k}}{2}$ lies on the plane 2x – 4y + z = 7, then what is the value of k ?

• 2

• 3

• 5

• 7

A point on the line $\frac{\mathrm{x} - 1}{1} = \frac{\mathrm{y} - 3}{2} = \frac{\mathrm{z} + 2}{7}$ has coordinates

• (3, 5, 4)

• (2, 5, 5)

• ( - 1,  - 1, 5)

• (2,  - 1, 0)

A point on a line has coordinates $\left(\mathrm{p} + 1, \mathrm{p} - 3, \sqrt{2}\mathrm{p}\right)$ where p is any real number. What are the direction cosines of the line ?

• $\frac{1}{2}, \frac{1}{2}, \frac{1}{\sqrt{2}}$

• $\frac{1}{\sqrt{2}}, \frac{1}{2}, \frac{1}{2}$

• $\frac{1}{\sqrt{2}}, \frac{1}{2}, - \frac{1}{2}$

• Cannot be determined due to insufficient data

What is the equation of the plane which cuts an intercept 5 units on the z-axis and is parallel to xy-plane ?

• x + y = 5

• z = 5

• z = 0

• x + y + z = 5

Into how many compartments do the coordinate planes divide the space ?

• 2

• 4

• 8

• 16

If a line has direction ratios < a + b, b + c, c + a >, then what is the sum of the square of its direction cosines ?

• (a + b + c)²

• 2(a + b + c)

• 3

• 1

27.

What is the perpendicular distance from the point (2, 3, 4) to the line $\frac{\mathrm{x} - 0}{1} = \frac{\mathrm{y} - 0}{0} = \frac{\mathrm{z} - 0}{0}$ ?

• 6 units

• 5 units

• 3 units

• 2

What is the length of the diameter of the sphere whose centre is at (1, - 2, 3) and which touches the plane 6x – 3y + 2z – 4 = 0 ?

• 1 unit

• 2 units

• 3 units

• 4 units