Angle Between Two Intersecting Lines

What does the term “Intersecting Lines” mean? 

The phrase ‘intersecting lines’ refers to a scenario in which two or more lines intersect in a plane and unite to form a single line. It is referred to as the point of the junction because the crossing lines all share a similar point, hence earning the term. When the lines, say P and Q connect, they form a point known as the junction of a line and a plane.

The intersection point

A line is a group of points that may be joined together endlessly in opposite directions.

A point is an unknown location on a plane with no dimensions, i.e. no width, length, or depth. The following linkages between two planes in a three-dimensional space are possible.

•   They may be next to one another
•   They may be the same or dissimilar in appearance
•   They could be able to communicate with one another

Characteristics of intersecting lines

Intersecting lines exhibit particular characteristics, they are –

•   Convergence occurs when two or more intersecting lines meet at a single location
•   The crossing lines may be perpendicular to one another. Regardless of the scenario, the magnitude of the resulting angle is always greater than 0° and less than 180°
•   Vertical angles are created when two intersecting lines produce a pair of vertical angles. Vertical angles are diametrically opposed angles that share a single vertex. In buildings, vertical angles are employed (which is the point of intersection)

 The angle created by two intersecting lines aids in comprehending the relationship between the two lines. It is a measure of the inclination angle formed by two parallel lines. Between two intersecting lines, two angles may be found, referred to as the acute and obtuse angles. 

By calculating the angle created by two lines, one may determine the angle formed by two sides of a closed polygon. To demonstrate how the formulas and examples for the angle between two lines in a coordinate plane and three-dimensional space operate, let us examine the formulas and examples for the angle between two lines in a coordinate plane and three-dimensional space.

How to Calculate the Angle Between Two Lines

When you know the slope of two lines, you can compute the angle between them; if you know their equation, you can calculate the angle between two lines. In most cases, the acute angle between two lines may be calculated from the angle between two lines.

Using the slope of two lines and the trigonometric tangent function, it is possible to determine the angle between two lines in two different ways. Consider two lines with slopes m1 and m2, respectively. The acute angle between the lines may be determined using the tangent function’s formula, which is shown below. The acute angle formed by the two lines may be calculated using the following formula.

The angle between two lines having equations  l1=a1x+b1y+c1=0,and I2=a2x+b2y+c2=0

θ=tan-1a2b1-a1b2a1a2+b1b2 

Angle between two intersecting lines

 The next section will examine how the angle between two straight lines is obtained and why it is significant. Bear in mind that when we discuss the angle between two lines, we are often referring to the angle between two intersecting lines, not to the angle between two straight lines. This is because the angle created by two perpendicular lines is defined as 90°, but the angle produced by two parallel lines is 0°.

 As a consequence, we’ll now examine how the angle between two intersecting lines is calculated. 

As the previous direction, cosine is the cosine of the angle made by the line in the three-dimensional space, with the x-axis, y-axis, z-axis respectively.
Let the two lines’ direction cosines be l1, m1,  n1 and l2 ,m2 , n2 respectively the angle between the two lines can be computed using the following formula:
cos = |l1.l2+m1.m2+n1.n2|