Find Unit Vector

[nycmath]

See attachment.

Show your work.

[Guest]

$|\vec{a}| = \sqrt{2^2 + 3^2 + 1^2} = \sqrt{14}$

$\hat{a} = \frac{\vec{a}}{|\vec{a}|} = \frac{2\hat{i} + 3\hat{j} + \hat{k}}{\sqrt{14}} \approx 0.535\hat{i} + 0.802\hat{j} + 0.267\hat{k}$

[nycmath]

$|\vec{a}| = \sqrt{2^2 + 3^2 + 1^2} = \sqrt{14}$

$\hat{a} = \frac{\vec{a}}{|\vec{a}|} = \frac{2\hat{i} + 3\hat{j} + \hat{k}}{\sqrt{14}} \approx 0.535\hat{i} + 0.802\hat{j} + 0.267\hat{k}$

Good but you did not explain what you did.

[Eigenvalue]

The unit vector is a vector with a magnitude of 1

1. Rewrite the vector on component form: (2,3,1)

2. Find the magnitude of the vector
||v||=[tex]\sqrt{i²+j²+k²}[/tex]

||v||=[tex]\sqrt{2²+3²+1²}[/tex]=[tex]\sqrt{14}[/tex]

3. Divide all components by the magnitude of the vector:
([tex]\frac{2}{ \sqrt{14} }[/tex], [tex]\frac{3}{ \sqrt{14} }[/tex], [tex]\frac{1}{ \sqrt{14} }[/tex])

([tex]\frac{2 \sqrt{14} }{14}[/tex], [tex]\frac{3 \sqrt{14} }{14}[/tex], [tex]\frac{\sqrt{14} }{14}[/tex])

([tex]\frac{ \sqrt{14} }{7}[/tex], [tex]\frac{3 \sqrt{14} }{14}[/tex], [tex]\frac{\sqrt{14} }{14}[/tex])

[nycmath]

The unit vector is a vector with a magnitude of 1

1. Rewrite the vector on component form: (2,3,1)

2. Find the magnitude of the vector
||v||=[tex]\sqrt{i²+j²+k²}[/tex]

||v||=[tex]\sqrt{2²+3²+1²}[/tex]=[tex]\sqrt{14}[/tex]

3. Divide all components by the magnitude of the vector:
([tex]\frac{2}{ \sqrt{14} }[/tex], [tex]\frac{3}{ \sqrt{14} }[/tex], [tex]\frac{1}{ \sqrt{14} }[/tex])

([tex]\frac{2 \sqrt{14} }{14}[/tex], [tex]\frac{3 \sqrt{14} }{14}[/tex], [tex]\frac{\sqrt{14} }{14}[/tex])

([tex]\frac{ \sqrt{14} }{7}[/tex], [tex]\frac{3 \sqrt{14} }{14}[/tex], [tex]\frac{\sqrt{14} }{14}[/tex])

Do you see how much clearer the math work is when using LaTex?