The foot of perpendicular from the point (3, 4, 5) to the plane x + y + z = 9 is

• (2, 3, 4)

• (3, 5, - 2)

• (3, 5, 2)

• (3, 2, 4)

The area of the parallelogram having the diagonals 3i + j - 2k and i - 3j + 4k is

• 5 sq units

• $10\sqrt{3} \mathrm{sq} \mathrm{units}$

• $5\sqrt{3} \mathrm{sq} \mathrm{units}$

• 10 sq units

The ratio in which yz-plane divide the line joining the points A(3, 1, - 5) and B(1, 4, - 6) is

• - 3 : 1

• 3 : 1

• - 1 : 3

• 1 : 3

If ${}^{\mathrm{n}}\mathrm{P}_5 = 20{}^{\mathrm{n}}\mathrm{P}_3$, then the value of n is

• 7

• 5

• 8

• 9

The equation of a straight line parallel to the x-axis is given by

• $\frac{\mathrm{x} - \mathrm{a}}{1} = \frac{\mathrm{y} - \mathrm{b}}{1} = \frac{\mathrm{z} - \mathrm{c}}{1}$

• $\frac{\mathrm{x} - \mathrm{a}}{0} = \frac{\mathrm{y} - \mathrm{b}}{0} = \frac{\mathrm{z} - \mathrm{c}}{1}$

• $\frac{\mathrm{x} - \mathrm{a}}{0} = \frac{\mathrm{y} - \mathrm{b}}{1} = \frac{\mathrm{z} - \mathrm{c}}{1}$

• $\frac{\mathrm{x} - \mathrm{a}}{1} = \frac{\mathrm{y} - \mathrm{b}}{0} = \frac{\mathrm{z} - \mathrm{c}}{0}$

The shortest distance between the lines

$\frac{\mathrm{x} - 3}{1} = \frac{\mathrm{y} - 5}{- 2} = \frac{\mathrm{z} - 7}{1}$ and $\frac{\mathrm{x} + 1}{1} = \frac{\mathrm{y} + 1}{- 6} = \frac{\mathrm{z} + 1}{1}$ is

• $\frac{1}{2}\sqrt{29} \mathrm{units}$

• $2\sqrt{29} \mathrm{units}$

• $\sqrt{29} \mathrm{units}$

• $\frac{1}{4}\sqrt{29} \mathrm{units}$

367.

The angle between the lines $\frac{\mathrm{x} - 2}{3} = \frac{\mathrm{y} + 1}{- 2}; \mathrm{z}= 2$ and $\frac{\mathrm{x} - 1}{1} = \frac{2\mathrm{y} + 3}{3}; \frac{\mathrm{z} +\hspace{0.17em}5}{2}$ is

• $\frac{\mathrm{\pi }}{3}$

• $\frac{\mathrm{\pi }}{6}$

• $\frac{\mathrm{\pi }}{2}$

• $\frac{\mathrm{\pi }}{4}$

The angle between planes 2x - y + z = 6 and x + y + 2z = 8 is

• 30°

• 60°

• ${\cos }^{-1}\left(\sqrt{\frac{3}{2}}\right)$

• ${\sin }^{-1}\sqrt{\left(\frac{3}{2}\right)}$

Equation of a plane passing through (- 1, 1, 1) and (1, - 1, 1) and perpendicular to x + 2y + 2z = 5 is

• 2x + 3y - 3z + 3 = 0

• x + y + 3z - 5 = 0

• 2x+ 2y - 3z + 3 = 0

• x + y + z - 3 = 0

The position vectors of three non-collinear points A, Band C are a, b and c, respectively. The perpendicular distance of point C from the straight line AB is

• $\frac{\left|\mathrm{b} \times \mathrm{c}\right|}{\left|\mathrm{b} - \mathrm{c}\right|}$

• $\frac{\left|\mathrm{a} \times \mathrm{b}\right|}{\left|\mathrm{b} - \mathrm{a}\right|}$

• $\frac{\left|\mathrm{c} \times \mathrm{a}\right|}{\left|\mathrm{c} - \mathrm{a}\right|}$

• $\frac{\left|\mathrm{b} \times \mathrm{c} + \mathrm{c} \times \mathrm{a} + \mathrm{a} \times \mathrm{b}\right|}{\left|\mathrm{b} - \mathrm{a}\right|}$