Question

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

A) If u= (u1,u2) with u(i) not equal to 0 for some 1< i < 2 ( both equal to i ) , then the unit vector in the direction of u is 1/ square root of u(1) squared + u(2) squared * (U(1), u(2)).

B) If u= (1,2,3) find the unit vector in the direction of u.

Answer 1

A) By the definition, unit vector: $\hat u=\frac{u}{||u||}=\frac{(u_1,u_2)}{\sqrt{u_1^2+u_2^2}}.$ True.

B) $\hat u=\frac{u}{||u||}=\frac{(u_1,u_2,u_3)}{\sqrt{u_1^2+u_2^2+u_3^2}}=\frac{(1,2,3)}{\sqrt{1^2+2^2+3^2}}=\frac{1}{\sqrt{14}}(1,2,3).$