Free Printable Inner product Spaces

1.

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

a)

$\sqrt{\frac{17}{16}}$

b)

$\sqrt{\frac{1025}{64}}$

c)

$\frac{\sqrt{577}}{4}$

d)

$\sqrt{\frac{17}{4}}$

2.

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

a)

$\sqrt{\frac{1025}{8}}$

b)

$\sqrt{\frac{1025}{64}}$

c)

$\frac{\sqrt{577}}{4}$

d)

$\sqrt{\frac{17}{4}}$

3.

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

a)

$\frac{\sqrt{577}}{64}$

b)

$\sqrt{\frac{1025}{64}}$

c)

$\frac{\sqrt{577}}{8}$

d)

$\sqrt{\frac{17}{4}}$

4.

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

a)

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

b)

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

c)

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

d)

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

5.

Find the distance between two vertors u and v.

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

a)

$\sqrt{3}$

b)

6

c)

3

d)

9

6.

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

a)

-6

b)

-30

c)

13

d)

25

7.

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

a)

-6

b)

-30

c)

13

d)

25

8.

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

a)

-6

b)

-30

c)

13

d)

25

9.

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

a)

(-12, 18)

b)

(12, 18)

c)

(-12, -18)

d)

(12, -18)

10.

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

a)

-6

b)

13

c)

25

d)

-30

11.

Find $\left(u+v\right)\ \circ\ \left(2u\ -\ v\right)$ .

$u\ \circ\ u\ =\ 4$

$u\ \circ\ v\ =\ -5$

$v\ \circ\ v\ =\ 10$

a)

7

b)

-7

c)

13

d)

-13

12.

Every Orthogonal set is linearly independent

a)

True

b)

False

13.

Every orthonormal set is linearly independent

a)

True

b)

False

14.

What is the distance between any two elements of an orthonormal set

a)

$\sqrt{2}$

b)

$\sqrt{3}$

c)

$\pi$

d)

$\infty$

15.

Are all linearly independent set Orthogonal?

a)

True

b)

False

Inner product Spaces

Total questions: 15

Worksheet time: 8mins

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