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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

Let us see the following implementation to get better understanding −

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))

0.42426, 0.56568, 0.7071

True

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