a. The vectors p and q are such that p = 11i – 24j and q = 2i + αj.

i. Find the value of each of the constants α and β such that p + 2q = (α + β)I – 20j.

ii. Using the values of α and β found in part I, find the unit vector in the direction p + 2q.

b.

The point A and B have position vectors a and b with respect to an origin O. The point C lies on AB and is such that AB: AC is 1: λ. Find an expression for OC(vector) in terms of a, b and λ.

c. The points S and T have position vectors s and t with respect to an origin O.

The point O, S and T do not lie in a straight line. Given that the vector 2s + µt is parallel to the vector (µ + 3)s + 9t where µ is a positive constant, find the value of µ.

Transcribed Image Text:

a C by B