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

• 3 : 7

• 2 : 7

• - 3 : 7

• - 2 : 7

732.

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

$\mathrm{If} 3\hat{\mathrm{i}} + 3\hat{\mathrm{j}} + \sqrt{3}\hat{\mathrm{k}}, \sqrt{3}\hat{\mathrm{i}} + \sqrt{3}\hat{\mathrm{j}} + \mathrm{\lambda }\hat{\mathrm{k}} \mathrm{are} \mathrm{coplaner}, \mathrm{then} \mathrm{\lambda } \mathrm{is} \mathrm{equal} \mathrm{to}$

• 1

• 2

• 3

• 4

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

• $\frac{\mathrm{\pi }}{4}$

• $\frac{\mathrm{\pi }}{3}$

• $\frac{\mathrm{\pi }}{2}$

• 0

If (2, - 1, 3) is the foot of the perpendicular drawn from the origin to the plane, then the equation of the plane is

• 2x + y - 3z + 6 = 0

• 2x - y + 3z - 14 = 0

• 2x - y + 3z - 13 = 0

• 2x + y + 3z - 10 = 0

If the plane 3x - 2y - z - 18 = 0 meets the coordinate axes in A, B, C then the centroid of $∆\mathrm{ABC}$ is

• (2, 3, - 6)

• (2, - 3, 6)

• (- 2, - 3, 6)

• (2, - 3, - 6)

The direction cosines of the line passing through P(2, 3, - 1) and the origin are

• $\frac{2}{\sqrt{14}}, \frac{{\displaystyle 3}}{{\displaystyle \sqrt{14}}}, \frac{{\displaystyle 1}}{{\displaystyle \sqrt{14}}}$

• $\frac{2}{\sqrt{14}}, \frac{{\displaystyle - 3}}{{\displaystyle \sqrt{14}}}, \frac{{\displaystyle 1}}{{\displaystyle \sqrt{14}}}$

• $\frac{- 2}{\sqrt{14}}, \frac{{\displaystyle - 3}}{{\displaystyle \sqrt{14}}}, \frac{{\displaystyle 1}}{{\displaystyle \sqrt{14}}}$

• $\frac{ 2}{\sqrt{14}}, \frac{{\displaystyle - 3}}{{\displaystyle \sqrt{14}}}, \frac{{\displaystyle - 1}}{{\displaystyle \sqrt{14}}}$

If the direction cosines of two lines are such that l + m + n = 0, l² + m² - n² = 0, then the angle between them is :

• $\mathrm{\pi }$

• $\frac{\mathrm{\pi }}{3}$

• $\frac{\mathrm{\pi }}{4}$

• $\frac{\mathrm{\pi }}{6}$