# (a) Compute ‖u‖, ‖v‖, and u ∙ v for the given vector in R3. (b) Verify the Cauchy-Schwarz inequality for the given pair of vector.

$=\sqrt{3i}+\pi +ck,v=4i-j-k$, where is a constant.
(a) Compute $‖u‖,‖v‖$, and $u×v$ for the given vector in R3.
(b) Verify the Cauchy-Schwarz inequality for the given pair of vector.

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pierretteA

Here $u=\sqrt{3}i+\pi j+ck,v=4i-j-k,$ where c is a constant. (a) $||u||=\sqrt{{\sqrt{3}}^{2}+{\pi }^{2}+{c}^{2}}=\sqrt{3+{\pi }^{2}+{c}^{2}}$
$||v||=\sqrt{{4}^{2}+1+1}=\sqrt{18}$
and
$u×v=\left(\sqrt{3i}+\pi j+ck\right)×\left(4i-j-k\right)=4\sqrt{3}-\pi -c.$
(b) $|u×v|=|4\sqrt{3}-\pi -c|\le \sqrt{3+{\pi }^{2}+{c}^{2}}\sqrt{1}8=||u||||v||.$