Question

Select all the correct answers. Which vectors are unit vectors?

Answer 1

Answer:

Step-by-step explanation:

$(-\frac{1}{3} \sqrt{\frac{7}{2} } )^2+(\frac{1}{3} \sqrt{\frac{13}{2} } )^2\\=\frac{1}{9} (\frac{7}{2} +\frac{13}{2} )\\=\frac{1}{9} (\frac{7+13}{2} )\\=\frac{1}{9} \times10\\=\frac{10}{9} \neq 1$

not a unit vector.

b.

$(\frac{1}{\sqrt{3} } )^2+(-\sqrt{\frac{2}{3} } )^2\\=\frac{1}{3} +\frac{2}{3} \\=\frac{1+2}{3} \\=\frac{3}{3} \\=1$

it is a unit vector.

c.

$(\frac{1}{2} \sqrt{\frac{5}{3} } )^2+(-\frac{1}{2} \sqrt{\frac{7}{3} } )^2\\=\frac{1}{4} (\frac{5}{3} +\frac{7}{3} )\\=\frac{1}{4} (\frac{5+7}{3} )\\=\frac{1}{4} (\frac{12}{3} )\\=\frac{1}{4} (4)\\=1$

it is a unit vector.

d.

$(\frac{3}{\sqrt{7} } )^2+(-\frac{2}{\sqrt{7} } )^2\\=\frac{9}{7} +\frac{4}{7} \\=\frac{9+4}{7} \\=\frac{13}{7} \neq 1$

it is not a unit vector.