Free Printable Skalarni produkt vektora

1.

Odredi skalarni produkt vektora $\overrightarrow{a}=\frac{1}{2}\overrightarrow{i}+2\overrightarrow{j}$ i $\overrightarrow{b}=-2\overrightarrow{i}+\overrightarrow{j}$ koristeći formulu $\overrightarrow{a}\cdot\overrightarrow{b}=x_a\cdot x_b+y_a\cdot y_b$

a)

1

b)

3

c)

-2

d)

-1

2.

Ako je $\left|\overrightarrow{a}\right|=2$ , $\left|\overrightarrow{b}\right|=1$ i $\angle\left(\overrightarrow{a},\overrightarrow{b}\right)=60°$ , odredi $\overrightarrow{a}\cdot\overrightarrow{b}$ . Sjeti se: $\overrightarrow{a}\cdot\overrightarrow{b}=\left|\overrightarrow{a}\right|\cdot\left|\overrightarrow{b}\right|\cdot\cos\angle\left(\overrightarrow{a},\overrightarrow{b}\right)$

a)

120°

b)

2

c)

1

d)

$\sqrt{2}$

3.

Ako je $\left|\overrightarrow{a}\right|=2$ , $\left|\overrightarrow{b}\right|=1$ i $\overrightarrow{a}\cdot\overrightarrow{b}=1$ , odredi $\angle\left(\overrightarrow{a},\overrightarrow{b}\right)$ . Sjeti se: $\overrightarrow{a}\cdot\overrightarrow{b}=\left|\overrightarrow{a}\right|\cdot\left|\overrightarrow{b}\right|\cdot\cos\angle\left(\overrightarrow{a},\overrightarrow{b}\right)$

a)

$\frac{1}{2}$

b)

$60°$

c)

$90°$

d)

$30°$

4.

Odredite skalarni produkt vektora $\overrightarrow{a}=-7\overrightarrow{i}+4\overrightarrow{j\ }\ i\ \ \overrightarrow{b}=12\overrightarrow{i}-3\ \overrightarrow{j}$

a)

84

b)

-84

c)

96

d)

-96

5.

Odredite kut između vektora $\overrightarrow{a}=-7\overrightarrow{i}+4\overrightarrow{j\ }\ \ i\ \ \ \overrightarrow{b}=12\overrightarrow{i\ }-3\overrightarrow{j}$

a)

$164\degree17`\ 29``$

b)

$166\degree12`$

c)

$45\degree34´15``$

d)

$123\degree34`23``$

6.

Za koji y su vektori $\overrightarrow{a}=-3\overrightarrow{i}+\overrightarrow{j\ }\ \ i\ \overrightarrow{\ b}=2\overrightarrow{i}-y\overrightarrow{j}$ okomiti?

a)

$-6$

b)

$3$

c)

$-3$

d)

$6$

Skalarni produkt vektora

Total questions: 6

Worksheet time: 30mins

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