Answer to Question #107156 in Analytic Geometry for Caylin

Question #107156

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.




1
Expert's answer
2020-03-31T13:57:22-0400

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)."


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