39. Let P, = t(3,2, l). (i) What is the distance from P, to (2,0,0)? (ii) For what value of z is the distance shortest? (iii) What is that shortest distance? The Dot Product Algebraic definition: (ajit bj+ c,k) . (azi + b2j + (2k) = ajaz + b, b2 + cic2. Geometric interpretation: V1 . V2 = IV, Il i/v 2 /|cos 0, where O is the angle between v, and v2, 0 0 for any vector u. 2. u . u = 0 only if u = 0. 3. u . v = v . u. 4. (utv) . w= u . w tv .W. 5. (au) . v = a(u . v). 6. Ju . v)