MATLAB

1. A force F is of magnitude 14 N and acts at the point A(3, 2, 4) in the direction of the vector −2i +6j +3k. Find the moment of the force about the point B(1, 5, −2). Find also the angle between F and |𝐴𝐵|

2. Points A, B, C have coordinates (1, 2, 1), (−1, 1, 3) and (−2, −2, -2) respectively.

Calculate the vector product 𝐴𝐵x𝐴𝐶, the angle BAC and a unit vector perpendicular
to the plane containing A, B and C. Hence obtain

1. the equation of the plane ABC;
2. the equation of a second plane, parallel to ABC, and containing the point D(1, 1, 1);
3. The shortest distance between the point D and the plane containing A, B and C.
4. Without using functions dot and cross, write your own script to compute the dot product and the vector product of 2 vectors.