# Check if it is possible to draw a straight line with the given direction cosines in Python

PythonServer Side ProgrammingProgramming

Suppose we have three direction cosines l, m and n in 3-D space, we have to check whether it is possible to draw a straight line with these direction cosines or not.

So, if the input is like l = 0.42426 m = 0.56568 n = 0.7071, then the output will be True as this the direction cosines of a vector {3, 4, 5}.

To solve this, we will follow some rule as

• l = cos(a), where a is angle between the straight line and x-axis
• m = cos(b), where b is angle between the straight line and y-axis
• n = cos(c), where c is angle between the straight line and z-axis
• l^2 + m^2 + n^2 = 1

To solve this, we will follow these steps −

• angle := l * l + m * m + n * n
• angle := round of the value of angle up to 8 decimal places
• if |1 - angle| < 0.0001, then
• return True
• return False

## Example

Let us see the following implementation to get better understanding −

Live Demo

def solve(l, m, n) :
angle = l * l + m * m + n * n
angle = round(angle, 8)
if abs(1 - angle) < 0.0001:
return True
return False
l = 0.42426
m = 0.56568
n = 0.7071
print (solve(l, m, n))

## Input

0.42426, 0.56568, 0.7071

## Output

True