Question

Which of the following statements is/are true? Explain why the false one is false.

A. If u = (u1; u2) with ui 6= 0 for some 1  i  2; then the unit vector in the direction of u is

p 1

u21

+u22

(u1; u2) : (2)

B. u = (1; 2; 3) is the unit vector in the direction of u: (

Answer 1

(A)True because unit vector in the direction of u is $p_1=\frac{u(u_1,u_2)}{\sqrt{u_1^2+u_2^2}}$

(B)False because u(1,2,3) is not the unit vector in the direction of (1,2,3), the vector v$(\frac{1}{\sqrt{14}},\frac{2}{\sqrt{14}},\frac{3}{\sqrt{14}})$ is the unit vector in the direction of (1,2,3).