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Linear Algebra

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Moderate

Visualizing Vector Operations: Scaling and Non-standard Position

LINALG-XFLNBK

Let $\boldsymbol{v}$ be a vector in $\mathbb{R}^2$ whose tail is positioned in the third quadrant and whose head is positioned in the first quadrant.

In which quadrant does the vector $3\boldsymbol{v}$ terminate, if $3\boldsymbol{v}$ is expressed in standard position?

A

First Quadrant

B

Second Quadrant

C

Third Quadrant

D

Third Quadrant

E

Cannot be determined from this information.