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arrow_back Are these statements True or False?

by Platinum
(106,962 points)
in Mathematics
16 views
(a) If each component of a vector in $R^{3}$ is doubled, the norm of that vector is doubled.

 

(b) In $R^{2}$, the vectors of norm 5 whose initial points are at the origin have terminal points lying on a circle of radius 5 centered at the origin.

 

(c) Every vector in $R^{n}$ has a positive norm.

 

(d) If $\mathbf{v}$ is a nonzero vector in $R^{n}$, there are exactly two unit vectors that are parallel to $\mathbf{v}$.

 

(e) If $\|\mathbf{u}\|=2,\|\mathbf{v}\|=1$, and $\mathbf{u} \cdot \mathbf{v}=1$, then the angle between $\mathbf{u}$ and $\mathbf{v}$ is $\pi / 3$ radians.

 

(f) The expressions $(\mathbf{u} \cdot \mathbf{v})+\mathbf{w}$ and $\mathbf{u} \cdot(\mathbf{v}+\mathbf{w})$ are both meaningful and equal to each other. $(\mathrm{g})$ If $\mathbf{u} \cdot \mathbf{v}=\mathbf{u} \cdot \mathbf{w}$, then $\mathbf{v}=\mathbf{w}$

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