Math  /  Algebra

Questionin Exercises 39 and 40 , find the vector v with the given magnitude and the same direction as uu.
39. v=2,u=3,3|\mathrm{v}|=2, \mathrm{u}=\langle 3,-3\rangle

Studdy Solution
Scale the unit vector to have a magnitude of 2.
The vector v \mathbf{v} is:
v=2×uunit=2×12,12=22,22=2,2 \mathbf{v} = 2 \times \mathbf{u}_{\text{unit}} = 2 \times \left\langle \frac{1}{\sqrt{2}}, \frac{-1}{\sqrt{2}} \right\rangle = \left\langle \frac{2}{\sqrt{2}}, \frac{-2}{\sqrt{2}} \right\rangle = \langle \sqrt{2}, -\sqrt{2} \rangle
The vector v \mathbf{v} with the given magnitude and the same direction as u \mathbf{u} is:
2,2 \boxed{\langle \sqrt{2}, -\sqrt{2} \rangle}

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