Mathematics : Three Dimensional Geometry

Angle between the planes x + y + 2z = 6 and 2x - y + z = 9 is

• $\frac{\mathrm{\pi }}{4}$

• $\frac{\mathrm{\pi }}{6}$

• $\frac{\mathrm{\pi }}{3}$

• $\frac{\mathrm{\pi }}{2}$

The value of $\mathrm{\lambda }$ for which the straight line $\frac{\mathrm{x} - \mathrm{\lambda }}{3} = \frac{\mathrm{y} - 1}{2 + \mathrm{\lambda }} = \frac{\mathrm{z} - 3}{- 1}$ may lie on the plane x - 2y = 0, is

• 2

• 0

• $- \frac{1}{2}$

• $\mathrm{there} \mathrm{is} \mathrm{no} \mathrm{such} \mathrm{\lambda }$

In a triangle PQR, $\angle \mathrm{PQR}, \angle \mathrm{R} = . \mathrm{If} \tan \left(\frac{\mathrm{P}}{2}\right) \mathrm{and} \tan \left(\frac{\mathrm{Q}}{2}\right)$ are roots of ax² + bx + c = 0, where a$\ne$ 0, then which one is true?

• c = a + b

• a = b + c

• b = a + c

• b = c

If C is the reflection of A (2, 4) in x-axis and B is the reflection of C in y-axis, then | AB | is

• 20

• 2√5

• 4√5

• 4

Find the angle subtended by the double ordinate of length 2a of the parabola y² = ax at its vertex.

The equation to the pairs of opposite sides of a parallelogram are x² - 5x + 6 = 0 and y² - 6y + 5. Find the equations its diagonals.

A common tangent to 9x² - 16y² = 144 and x² + y² = 9 is

• $\mathrm{y} = \frac{3}{\sqrt{7}}\mathrm{x} + \frac{15}{\sqrt{7}}$

• $\mathrm{y} = 3\sqrt{\frac{2}{7}}\mathrm{x} + \frac{15}{\sqrt{7}}$

• $\mathrm{y} = 2\sqrt{\frac{3}{7}}\mathrm{x} + 15\sqrt{7}$

• None of these

The locus of a point P which moves such that 2PA = 3PB, where A(0, 0) and B(4,- 3) are points, is

• 5x² - 5y² - 72x + 54y + 225 = 0

• 5x² + 5y² - 72x + 54y + 225 = 0

• 5x² + 5y² + 72x - 54y + 225 = 0

• 5x² + 5y² - 72x - 54y - 225 = 0

The points P is equidistant from A(1, 3), B (- 3, 5) and C(5, - 1), then PA is equal to

• 5

• $5\sqrt{5}$

• 25

• $5\sqrt{10}$

The equation of the plane through the intersection of the planes x + y + z = 1 and 2x + 3y - z + 4 = 0 and parallel to X-axis, is

• y - 3z + 6 = 0

• 3y - z + 6 = 0

• y + 3z + 6 = 0

• 3y - 2z + 6 = 0