Pre Calculus

Question

If vector v has an initial point at P1 and a terminal point at P2, write v as multiples of the basis vectors i=⟨1,0⟩and j=⟨0,1⟩That is, write v in the form v = ai + bj.
P1 = (5, 2), P2 = (7, 11) and v = ?


a) v = 12i + 13j
b) v = 16i + 9j
c) v = 2i + 9j
d) v = −2i − 9j

Answer 1

Michael,

The basis, or unit vectors are like single steps in the i or j directions. So, if from P1 to P2 the i-component increases from 5 to 7, then we want an increase of 2i. The j-component increases from 2 to 11, so an increase of 9j.

 

Therefore, the vector v can be expressed as v = 2i+9j

 

 

Answer 2

v = (7-5)i + (11-2)j = 2i + 9j