Mathematics : Three Dimensional Geometry

A gun projects a ball at the angle of 45° with the horizontal. If the horizontal range is 39.2 m, then the ball will rise to

• 9.8 m

• 4.9 m

• 2.45 m

• 19.6 m

The angle between two diagonals of a cube will be

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

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

• variable

• None of these

The lines $\frac{\mathrm{x} - \mathrm{a} + \mathrm{d}}{\mathrm{\alpha } - \mathrm{\delta }} = \frac{\mathrm{y} - \mathrm{a}}{\mathrm{\alpha }} = \frac{\mathrm{z} - \mathrm{a} - \mathrm{d}}{\mathrm{\alpha } + \mathrm{\delta }}$ and $\frac{\mathrm{x} - \mathrm{b} + \mathrm{c}}{\mathrm{\beta } - \mathrm{\tau }} = \frac{\mathrm{y} - \mathrm{b}}{\mathrm{\beta }} = \frac{\mathrm{z} - \mathrm{b} - \mathrm{c}}{\mathrm{\beta } + \mathrm{\tau }}$ are coplanar and then equation to the plane in which they lie, is

• x + y + z = 0

• x - y + z = 0

• x - 2y + z = 0

• x + y - 2z = 0

Two parallel unlike forces of magnitudes 15N and 10N are acting at points A and B respectively. If C is the point of action of resultant, then AB/BC is

• 2/1

• 1/2

• 2/3

• 3/2

If a person A is moving with velocity 2 km/h, person B is moving with velocity 3 km/h and the angle between the direction of movements of A and B is 60°, then the velocity of A relative to B in the direction of A is

• $\sqrt{13 - 6\sqrt{3}}$

• $\sqrt{13 + 6\sqrt{3}}$

• $\sqrt{7}$

• $\sqrt{19}$

The intersection angle of the curve xy = a² and x² - y² = a² is

• $\frac{\mathrm{\pi }}{3}$

• $\frac{\mathrm{\pi }}{6}$

• $\frac{\mathrm{\pi }}{2}$

• $\frac{5\mathrm{\pi }}{6}$

The point of intersection of line $\frac{\mathrm{x} - 6}{- 1} = \frac{\mathrm{y} + 1}{0} = \frac{\mathrm{z} + 3}{4}$ and plane x + y - z = 3 is

• (2, 1, 0)

• (7, - 1, - 7)

• (1, 2, - 6)

• (5, - 1, 1)

A particle is thrown with the velocity v with the angle a from the horizontal plane and its range on the horizontal plane is twice to themaximum height gained. Then, $\tan \left(\mathrm{\alpha }\right)$ is equal to

• 9

• 5

• 2

• 1

The points 0, 2 + 3i, i - 2 - 2i in the argand plane are the vertices of a

• rectangle

• rhombus

• trapezium

• parallelogram

If the resultant of two forces of magnitude P and P$\sqrt{3}$ acting on a particle is of magnitude P, then the angle between them is

• 60°

• 120°

• 90°

• 150°