Inner product Spaces

u = (-1, 1/4) and v = (4, -1/8). find  $\parallel u\parallel$  .

•  $\sqrt{\frac{17}{16}}$  

•  $\sqrt{\frac{1025}{64}}$  

•  $\frac{\sqrt{577}}{4}$  

•  $\sqrt{\frac{17}{4}}$  

u = (-1, 1/4) and v = (4, -1/8). find  $\parallel v\parallel$  .

•  $\sqrt{\frac{1025}{8}}$  

•  $\sqrt{\frac{1025}{64}}$  

•  $\frac{\sqrt{577}}{4}$  

•  $\sqrt{\frac{17}{4}}$  

u = (-1, 1/4) and v = (4, -1/8). find  $\parallel u+v\parallel$  .

•  $\frac{\sqrt{577}}{64}$  

•  $\sqrt{\frac{1025}{64}}$  

•  $\frac{\sqrt{577}}{8}$  

•  $\sqrt{\frac{17}{4}}$  

find the unit vector in the direction u.u = (3, 2, -5)

•  $\left(\frac{3}{\sqrt{38}},\ \frac{2}{\sqrt{38}},\ \frac{5}{\sqrt{38}}\right)$  

•  $\left(\frac{3}{\sqrt{38}},\ \frac{-2}{\sqrt{38}},\frac{-5}{\sqrt{38}}\right)$  

•  $\left(\frac{-3}{\sqrt{38}},\ \frac{-2}{\sqrt{38}},\ \frac{-5}{\sqrt{38}}\right)$  

•  $\left(\frac{3}{\sqrt{38}},\ \frac{2}{\sqrt{38}},\ \frac{-5}{\sqrt{38}}\right)$  

Find the distance between two vertors u and v.

u = (1, 2, 0) and v = (-1, 4, 1)

• $\sqrt{3}$

• 6

• 3

• 9

Find the dot product  $u\ \circ\ v$  
u = (3, 4) and v = (2, -3)

• -6

• -30

• 13

• 25

Find the dot product  $v\ \circ\ v$  
u = (3, 4) and v = (2, -3)

• -6

• -30

• 13

• 25

Find the dot product  $\parallel u\parallel^2$  
u = (3, 4) and v = (2, -3)

• -6

• -30

• 13

• 25

Find the dot product  $\left(u\ \circ\ v\right)v$  
u = (3, 4) and v = (2, -3)

• (-12, 18)
  

• (12, 18)
  

• (-12, -18)
  

• (12, -18)
  

Find the dot product  $u\ \circ\ 5v$  
u = (3, 4) and v = (2, -3)

• -6

• 13

• 25

• -30