Free Printable Vectori. Operatii cu vectori

1.

Fie ABC un triunghi si punctele M, N definite prin $\overrightarrow{AM}=\frac{1}{3}\overrightarrow{AB},\ \overrightarrow{AN}=\frac{2}{3}\overrightarrow{AC}$ . Atunci:

a)

$\overrightarrow{MN}=\frac{1}{3}\left(\overrightarrow{CB}-\overrightarrow{AC}\right)$

b)

$\overrightarrow{MN}=\frac{2\overrightarrow{AC}}{3}-\frac{\overrightarrow{AB}}{3}$

c)

$\overrightarrow{MN}=\frac{2}{3}\overrightarrow{BC}$

d)

$\overrightarrow{MN}=\frac{1}{2}\overrightarrow{BC}-\frac{1}{3}\overrightarrow{AC}$

2.

Fie M un punct pe latura BC a triunghiului ABC. Care dintre relatiile urmatoare este corecta?

a)

$\overrightarrow{AB}+\overrightarrow{BM}=\overrightarrow{AC}+\overrightarrow{CM}$

b)

$\overrightarrow{AB}+\overrightarrow{AC}=2\overrightarrow{AM}$

c)

$\overrightarrow{AM}+\overrightarrow{AB}+\overrightarrow{AC}=\overrightarrow{0}$

d)

$\overrightarrow{AM}+\overrightarrow{AC}+\overrightarrow{AB}=\overrightarrow{MC}$

3.

In planul cartezian se considera vectorii coliniari $\overrightarrow{u}=k\overrightarrow{i}+2\overrightarrow{j},\ \ \overrightarrow{v}=\overrightarrow{i}-3\overrightarrow{j}$ . Atunci:

a)

$k=-3$

b)

$k=\frac{2}{3}$

c)

$k=-\frac{2}{3}$

d)

$k=1$

4.

Se considera vectorii $\overrightarrow{u}=\overrightarrow{i}+\overrightarrow{j},\ \ \ \overrightarrow{v}=\overrightarrow{i}-2\overrightarrow{j},\ \ \overrightarrow{w}=\overrightarrow{u}+\overrightarrow{v}$ . Fie $\alpha=\left|\overrightarrow{w}\right|$ . atunci:

a)

$\alpha=1$

b)

$\alpha=\sqrt{5}$

c)

$\alpha=\sqrt{3}$

d)

$\alpha=-1$

5.

Fie A(2,3) si B(4,-1). Sa se afle coordonatele punctului M pentru care $\overrightarrow{MA}+\overrightarrow{MB}=0$

a)

$\left(1,1\right)$

b)

$\left(2,1\right)$

c)

$\left(3,1\right)$

d)

$\left(1,3\right)$

6.

Se dau vectorii $\overrightarrow{u}=\left(\beta-1\right)\overrightarrow{i}-3\overrightarrow{j}\ \ si\ \ \overrightarrow{v}=\beta\overrightarrow{i}+\overrightarrow{j}$ . Sa se determine $\beta\in R$ , astfel incat $\overrightarrow{u}\ \ si\ \ \overrightarrow{v}$ sa fie paraleli.

a)

$1$

b)

$\frac{1}{2}$

c)

$\frac{1}{4}$

d)

$4$

7.

Fie un paralelogram ABCD de centru O. Daca M este un punct arbitrar din planul paralelogramului, atunci este valabila relatia vectoriala $\overrightarrow{MA}+\overrightarrow{MB}+\overrightarrow{MC}+\overrightarrow{MD}=k\cdot\overrightarrow{MO}$ pentru constanta k egala cu...

a)

1

b)

2

c)

3

d)

4

8.

In planul $xOy$ se considera paralelogramul ABCD in care M este punctul de intersectie al diagonalelor, iar N este mijlocul laturii CD. Daca $\overrightarrow{AB}=\overrightarrow{i}+\overrightarrow{j}\ \ si\ \ \overrightarrow{AM}=2\overrightarrow{i}-\overrightarrow{j}$ , atunci:

a)

$\overrightarrow{AN}=\overrightarrow{i}+\overrightarrow{j}$

b)

$\overrightarrow{AN}=\frac{1}{2}\overrightarrow{i}-\frac{1}{2}\overrightarrow{j}$

c)

$\overrightarrow{AN}=\frac{7}{2}\overrightarrow{i}-\frac{5}{2}\overrightarrow{j}$

d)

$\overrightarrow{AN}=\frac{3}{2}\overrightarrow{i}+\frac{5}{2}\overrightarrow{j}$

9.

Dat fiind triunghiul ABC consideram punctele M, N, P definite prin $\overrightarrow{AP}=\frac{1}{3}\overrightarrow{AB},\ \ \overrightarrow{AN}=\frac{1}{2}\overrightarrow{AC},\ \overrightarrow{CM}=k\cdot\overrightarrow{BC},\ k\in R$ Punctele M,N,P sunt coliniare pentru:

a)

$k=-1$

b)

$k=1$

c)

$k=2$

d)

$k=-\frac{1}{2}$

Vectori. Operatii cu vectori

Total questions: 9

Worksheet time: 1hrs 15mins

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