Question 1 give examples of three vectors that are

Question

Question 1: Give examples of THREE vectors that are collinear and prove it.

Question 2: Given vectors "a"=[1, -3, 6] and "b"=[4, -5, -2], find a vector "c" so that a*(bxc)=0. Explain what is the relationship between the vectors a, b, and c in this case, and why? Verify this.

Question 3: a, b, and c are vectors. Prove that a*(b+c)=a*b+a*c for all a, b, c ∈ R³

Question 4: DRAW DIAGRAMS to explain the answers to the following questions.

a) Is it possible to have p_a(b)=0 ?

b) Is it possible to have p_a(b) undefined?

c) Is it possible to have p_a(b)= p_b(a) ?

e) Explain why p_a(c)=p_a(p_b(c))?