Answer to Question #115616 in Analytic Geometry for Rothama

Question

If v∈R2 lies in the first quadrant and makes an angle π/4 with the positive x-axis and ||v||=2, then, Select one:


a. v=⟨2√2, 2√2⟩


b. v=⟨2, 2√3⟩


c. v=⟨√2, √2⟩


d. v=⟨2, −2√3⟩


e. v=⟨2√2, −√2⟩

Answer 1

c)$v=(\sqrt{2};\sqrt{2})$

$v$ lies in the first quadrant, hence $x\ge 0$ and $y\ge 0$

$||v||=\sqrt{(\sqrt{2})^2+(\sqrt{2})^2}=\sqrt{4}=2$