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

−−→CB.

(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.-5i-8j-3k

(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?