The correct magnitude of the vector times the appropriate unit vector of given vectors are given as follows:
a. <0.708, 0, -0.708> [tex]*4.66*10^{-3}[/tex]
b. <0, -1, 0>*676
c. [tex]\overrightarrow{C} = <0.707, 0, -0.707>*4.47*10^2[/tex]
The general vector can be represented as:
[tex]\underset{A}{\rightarrow}[/tex] = (a, b, c) ......1
the magnitude [tex]| \right\underset{A}{\rightarrow} |[/tex] can be obtained as :
[tex]| \right\underset{A}{\rightarrow} | = \sqrt{a^{2}+ b^{2} +c^{2} }[/tex] .....2
and unit vector would be:
[tex]\hat{u}_A=\dfrac{\overrightarrow{A}}{|\overrightarrow{A}|}[/tex].......3
Solution:
a) ( 0.00330, 0, -0.00330)
here,
[tex]\underset{A}{\rightarrow} = ( 0.00330, 0, -0.00330)[/tex]
applying this magnitude to equation two:
[tex]| \right\underset{A}{\rightarrow} | = \sqrt{0.00330^{2}+ 0^{2} +(-0.00330)^{2} }[/tex] = [tex]4.66*10^{-3}[/tex]
the unit vector would be:
[tex]\hat{u}_A=\dfrac{\overrightarrow{A}}{|\overrightarrow{A}|}[/tex]
[tex]\hat{u}_A= < \frac{0.00330}{4.66*10^{-3}}, \frac{0}{4.66*10^{-3}}, \frac{-0.00330}{4.66*10^{-3}}>[/tex]
[tex]\hat{u}_A= <708, 0, -708>[/tex]
Thus, the vector [tex]{\overrightarrow{A}[/tex] would be - <0.708, 0, -0.708> [tex]*4.66*10^{-3}[/tex]
B) (0, -676, 0)
Solving simailarly like A),
Vector [tex]| \right\underset{B}{\rightarrow} | = \sqrt{0^{2}+ -676^{2} +0^{2} }[/tex] = 676
the unit vector would be:
[tex]\hat{u}_B=\dfrac{\overrightarrow{B}}{|\overrightarrow{B}|}\\\hat{u}_B= < \frac{0}{676}, \frac{-676}{676}, \frac{0}{676}>[/tex]
Thus, the vector [tex]\overrightarrow{B}[/tex] = <0, -1, 0>*676
C) (0.00316, 0, -0.00316)
Attempting the third vector similarly we will get magnitude:
[tex]| \right\underset{C}{\rightarrow} | = \sqrt{0.00316^{2}+ 0^{2} +(-0.00316)^{2} }[/tex] = [tex]*4.47*10^{-3}[/tex]
Then,
[tex]\hat{u}_C=\dfrac{\overrightarrow{C}}{|\overrightarrow{C}|}\\\hat{u}_C= < \frac{0.00316}{4.47*10^2}, \frac{0}{4.47*10^2}, \frac{0.00316}{4.47*10^2}>[/tex]
The vector [tex]\overrightarrow{C} = <0.707, 0, -0.707>*4.47*10^2[/tex]
Learn more about vector unit:
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