List of top Mathematics Questions on Geometry asked in Bihar Board XII

Equation of a plane parallel to the plane \( 9x - 8y + 7z = 10 \) is:

Through which of the following points does the line \[ \frac{x-11}{12} = \frac{y-12}{13} = \frac{z+13}{14} \text{ pass?} \]

If the direction ratios of two parallel lines are 2, 7, 9, then the value of x is:

If the direction ratios of two parallel lines are \( a, b, c \) and \( x, y, z \), then \( az = \dots \)?

If the direction ratios of two mutually perpendicular lines are 5, 2, 4 and 4, 8, x, then the value of x is:

The angle between two planes \( 2x + y - 2z = 5 \) and \( 3x - 6y - 2z = 7 \) is:

The distance of the plane \( x - 2y + 4z = 9 \) from the point \( (2, 1, -1) \) is:

If two planes \( 2x - 4y + 3z = 5 \) and \( x + 2y + \lambda z = 12 \) are mutually perpendicular to each other, then \(\lambda =\):

If the line \[ \frac{x - 3}{a} = \frac{y - 4}{b} = \frac{z - 5}{c} \] is parallel to the line \[ \frac{x}{5} = \frac{y}{3} = \frac{z}{2} \] then:

If the line \[ \frac{x - x_1}{a_1} = \frac{y - y_1}{b_1} = \frac{z - z_1}{c_1} \] is parallel to the plane \[ a_2 x + b_2 y + c_2 z + d = 0 \] then:

If \[ \frac{x}{18} = \frac{6}{18} \] then \(x\) is equal to:

The direction ratios of two straight lines are \( l, m, n \) and \( l_1, m_1, n_1 \). The lines will be perpendicular to each other if:

The direction ratios of a straight line are \( 1, 3, 5 \). Then its direction cosines are:

The equation of the plane parallel to the plane \( 3x - 5y + 4z = 11 \) is: