Free Printable Vektori 2

1.

$dane\ su\ točke\ A\left(-2,1\right),\ B\left(4,4\right),\ C\left(4,0\right),\ D\left(x,7\right).\ Vektori\ \overrightarrow{AB\ }i\ \ \overrightarrow{CD}\ \ \ su\ okomiti\ ako\ je:$

a)

x = 2

b)

x = -1

c)

x = 0

d)

$x\ =\ \frac{1}{2}$

2.

Koja od sljedećih formula NIJE povezana sa definicijom i svojstvima skalarnog umnoška?

a)

$\overrightarrow{a}\cdot\overrightarrow{b}=\left|\overrightarrow{a}\right|\cdot\left|\overrightarrow{b}\right|\cdot\cos\angle\left(\overrightarrow{a},\overrightarrow{b}\right)$

b)

$\overrightarrow{a}\cdot\overrightarrow{b}=a_x\cdot b_x+a_y\cdot b_y$

c)

$\left|\overrightarrow{a}\right|=\sqrt{a_x^2+a_y^2}$

d)

$\overrightarrow{a}\cdot\overrightarrow{b}=\overrightarrow{b}\cdot\overrightarrow{a}$

3.

Vektori

\overrightarrow{i}

i

\overrightarrow{j}

su

a)

jedinični vektori

b)

nulvektori

4.

Skalarni umnožak okomitih vektora je

a)

$0$

b)

$1$

5.

Koji je od navedenih vektora prikazan na slici?

a)

$\overrightarrow{AB}=-3\overrightarrow{i}+4\overrightarrow{j}$

b)

$\overrightarrow{AB}=3\overrightarrow{i}+4\overrightarrow{j}$

c)

$\overrightarrow{AB}=3\overrightarrow{i}-4\overrightarrow{j}$

d)

$\overrightarrow{AB}=-3\overrightarrow{i}-4\overrightarrow{j}$

6.

Zadani su vektori $\overrightarrow{a}=2\overrightarrow{i}-3\overrightarrow{j}$ i $\overrightarrow{b}=-\overrightarrow{i}-7\overrightarrow{j}$ . Kolika je mjera kuta između vektora $\overrightarrow{c}$ i $\overrightarrow{d}$ ako vrijedi $\overrightarrow{c}=\overrightarrow{a}+\overrightarrow{b}$ , $\overrightarrow{d}=\overrightarrow{a}-\overrightarrow{b}$ ?

a)

68°32´

b)

129°45´

c)

137°25´

d)

14°38´

e)

98°25´

7.

Za koji su realan broj k vektori $\overrightarrow{a}=-\overrightarrow{i}+7\overrightarrow{j}$ i $\overrightarrow{b}=k\overrightarrow{i}+4\overrightarrow{j}$ okomiti?

(a)

8.

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

9.

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)

$\sqrt{2}$

10.

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)

$30°$

Vektori 2

Total questions: 10

Worksheet time: 14mins

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