Linear Algebra for Computer Science

Question

Suppose we are given p,q are in Euclidean E² and v,w are in all real numbers R². Do the following operations result in a point or a vector?

A. p-q

B. 1/2p+1/2q

C. p+v

D. 3v

E. v+w

F. p+1/2w

Answer 1

p = (p1,p2)

q = (q1,q2)

p1,p2,q1,q2,v,w are real

A) p-q = (p1-q1, p2-q2) is a vector

B) 1/2p + 1/q = (p1/2 , p2/2) - (q1/2 , q2/2)

= ( (p1-q1)/2, (p2-q2)/2) is a vector

C) p+v = (p1,p2) +v is not allowed

D) 3v is a real number

E) V+w is a real number

F) p + w/2 = (p1,p2) + w/2 is not allowed