Compute the length of the given vector.
-$\mathrm { p } ( \mathrm { t } ) = 13 \mathrm { t } ^ { 2 }$ and $\mathrm { q } ( \mathrm { t } ) = \mathrm { t } - 1$, where $\mathrm { t } _ { 0 } = 0 , \mathrm { t } _ { 1 } = \frac { 1 } { 2 } , \mathrm { t } _ { 2 } = 1$
A) $\| \mathrm { p } \| = 0.5 \sqrt { 70 } ; \| \mathrm { q } \| = \sqrt { \frac { 5 } { 4 } }$
B) $\| \mathrm { p } \| = \sqrt { \frac { 5 } { 4 } } ; \| \mathrm { q } \| = 13 \sqrt { \frac { 5 } { 4 } }$
C) $\| \mathrm { p } \| = 13 \sqrt { 17 } ; \| \mathrm { q } \| = \sqrt { \frac { 5 } { 4 } }$
D) $\| \mathrm { p } \| = \frac { 13 } { 4 } \sqrt { 17 } ; \| \mathrm { q } \| = \sqrt { \frac { 5 } { 4 } }$

Question

Quizplus · Accepted Answer

The length of vector $\mathrm{p}$ is calculated using the integral of the square root of the sum of squares of derivatives over the interval $[t_0, t_2]$. Similarly, the length of $\mathrm{q}$ is calculated, resulting in $\| \mathrm{q} \| = \sqrt{\frac{5}{4}}$.

Compute the Length of the Given Vector p(t)=13t2\mathrm { p } ( \mathrm { t } ) = 13 \mathrm { t } ^ { 2 }p(t)=13t2

Compute the Length of the Given Vector $\mathrm { p } ( \mathrm { t } ) = 13 \mathrm { t } ^ { 2 }$