Answer
$C) 3$
d) $\sqrt{3}$
a) $5 \quad$ b) 3
Work Step by Step
The norm of a given vector in $n$ -space:
\[
\vec{v}=\left\langle a_{1}, a_{2}, \ldots, a_{n}\right\rangle
\]
is $\|\vec{v}\|=\sqrt{a_{1}^{2}+a_{2}^{2}+\cdots+a_{n}^{2}},$ and then
a) For ( 3,4 ) we have that:
\[
\|\vec{v}\|=\sqrt{4^{2}+3^{2}}=\sqrt{16+9}=5
\]
b) For $\vec{v}=-\sqrt{7} \hat{\jmath}+\sqrt{2} \hat{\imath} =\langle\sqrt{2},-\sqrt{7}\rangle$ we have:
\[
\|\vec{v}\|=\sqrt{(\sqrt{2})^{2}+(-\sqrt{7})^{2}}=\sqrt{7+2}=3
\]
c) For $\vec{v}=\rangle 0,-3,0\langle$ we have:
\[
\|\vec{v}\|=\sqrt{(-3)^{2}+0^{2}+0^{2}}=\sqrt{9}=3
\]
d) For $\vec{v}=\hat{\imath}+\hat{\jmath}+\hat{k}=\langle 1,1,1\rangle$ we have:
\[
\|\vec{v}\|=\sqrt{1^{2}+1^{2}+1^{2}}=\sqrt{3}
\]
