Determine whether the following are true or false Explain yo

Determine whether the following are true or false. Explain your answers. a. If u and v have the same magnitude and directions, then u = v. b. If v = ai + bj = 0, then a = -b. c. If u = ai + bj is a unit vector, then a^2 + b^2 = 1.

Solution

a. If the vectors have same magnitude and direction then vectors are equal .Therefore u=v is true .

b. v=0 means magnitude is zero. So it is not necessary that a=-b. hence it is false .

c. For a unit vetor , magnitude=1, therefore a²+b²=1 is true .