Calculate the angle between straight lines MN and KL if M (2; 0; 1) N (-2; 1; 2) K (0; 3; -2) L (-4; 0; 1).

univerkov | April 9, 2021 | education

1) Find the coordinates of the vectors MN and KL. To do this, subtract the coordinates of its beginning from the coordinates of the end of the vector. We have: MN = {-2 – 2; 10; 2 – 1} = {-4; one; 1}, KL = {-4 – 0; 0 – 3; 1 – (-2)} = {-4; -3; 3}.
2) Now we find the scalar product of these vectors and their lengths: | MN | = √ ((- 4) 2 + 12 + 12) = 3√2, | KL | = √ ((- 4) 2 + (-3) 2 + 32) = √ (34), MN * KL = (-4) * (-4) + 1 * (-3) + 1 * 3 = 16.
3) Now you can cosine the angle between the straight lines: cos (φ) = (MN * KL) / (| MN | * | KL |) = 8√ (17) / 51.
ANSWER: 8√ (17) / 51.

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