Vector Help Needed

[justsomeguy]

So here's the question:

Find the normal to the plane containing the points A(2, 5, −2), B(−4, 6, 1) and C(6, −3, 7) and verify that this normal vector is perpendicular to any vectors of the form V = αAB + βAC for any real numbers α and β.

So I started by forming vectors AB and AC and used the 3x3 determinant or cross product or whatever to find the normal but I'm not sure how to go about the second part of verifying the orthogonality

 

[lev888]

2 vectors are orthogonal if?

 

[justsomeguy]

Two vectors would be orthogonal/perpendicular if their dot product is equal to zero

 

[lev888]

Write out the dot product expression for the normal vector you found and αAB + βAC - you should get 0.