Test: Geometrical Shapes and Solids - 2 - Class 4 MCQ

Mensuration in geometry involves the calculation of various measurements such as perimeter (distance around a shape), area (space occupied by a flat shape), and volume (space occupied by a solid object).

Analytical geometry is also known as coordinate geometry, as it involves the use of coordinates and algebraic equations to study geometric objects.

Points on a plane in analytical geometry are defined using coordinates, which are ordered pairs of numbers representing the position of a point.

The direction cosines of a line are denoted by l, m, and n, and they represent the cosines of the angles the line makes with the x-axis, y-axis, and z-axis, respectively.

The angle between two lines can be calculated using the formula cos θ = |l1l2 + m1m2 + n1n2|, where l1, m1, n1 and l2, m2, n2 are the direction cosines of the two lines.

The vector equation of a line passing through a point with the position vector → a and parallel to vector → b is given by → r = → a + λ → b, where λ is a scalar parameter.

The formula cos θ = |l1 + m1 + n1| is not used to calculate the angle between two lines. The correct formula is cos θ = |l1l2 + m1m2 + n1n2|.

A triangle is a two-dimensional shape, not a three-dimensional shape. It lies in a plane and has three sides and three vertices.

Depth is not considered in three-dimensional geometry. The three dimensions considered are length, width, and height.

The distance formula, section formula, midpoint formula, and other calculations in coordinate geometry are based on analytical equations that involve coordinates and algebraic expressions. These formulas help determine geometric properties using numerical calculations.