Suppose a point A has co-ordinates (−1, 3, 5), a point B has co-ordinates
(0, −3, 2), and another point C has co-ordinates (−5, −5, −5).
(a) Find −→BA and −−→CB.
BA(1, 0, -7)
CB(5, 8, 3)
(b) Find −→BA − 3
(16, 24, 16)
(c) Use the result of part (b) to write −→BA − 3
−−→CB as a multiple of the vector (8, 0, 9).??? DON'T GET THIS PART
(d) Express −−→CB in terms of the standard unit vectors i, j and k.
(e) Use the result of part (a) to ﬁnd −→AC.
(f) Verify the triangle inequality: ||−→AB +
−−→BC|| ≤ ||−→AB|| + ||−−→BC||.
(g) Find a unit vector pointing in the same direction as −→AB.
(h) How far is the point C from the origin?