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  1. Home
  2. 12th grade
  3. Trigonometry
  4. Exercise : Determine to which condition a vector is colinear to a given vector

Determine to which condition a vector is colinear to a given vector Trigonometry

In which condition are \overrightarrow{u}=\dbinom{a}{4} and \overrightarrow{v}=\dbinom{3}{6} collinear ?

Two vectors \overrightarrow{u}=\dbinom{a}{b} and \overrightarrow{v}=\dbinom{c}{d} are collinear if and only if ad = bc. Therefore, the vectors are collinear if:

6 \times a = 4 \times 3

6a=12

a=2

\overrightarrow{u} and \overrightarrow{v} are colinear if and only if a=2.

In which condition are \overrightarrow{u}=\dbinom{-3}{4} and \overrightarrow{v}=\dbinom{\dfrac{3}{2}}{a} collinear ?

Two vectors \overrightarrow{u}=\dbinom{a}{b} and \overrightarrow{v}=\dbinom{c}{d} are collinear if and only if ad = bc. Therefore, the vectors are collinear if:

-3 \times a = 4 \times \dfrac{3}{2}

-3a=6

a=-2

\overrightarrow{u} and \overrightarrow{v} are colinear if and only if a=-2.

In which condition are \overrightarrow{u}=\dbinom{a}{10} and \overrightarrow{v}=\dbinom{2}{5} collinear ?

Two vectors \overrightarrow{u}=\dbinom{a}{b} and \overrightarrow{v}=\dbinom{c}{d} are collinear if and only if ad = bc. Therefore, the vectors are collinear if:

5 \times a = 2 \times 10

5a=20

a=4

\overrightarrow{u} and \overrightarrow{v} are colinear if and only if a=4.

In which condition are \overrightarrow{u}=\dbinom{a}{6} and \overrightarrow{v}=\dbinom{-5}{-10} collinear ?

Two vectors \overrightarrow{u}=\dbinom{a}{b} and \overrightarrow{v}=\dbinom{c}{d} are collinear if and only if ad = bc. Therefore, the vectors are collinear if:

-10 \times a = 6 \times\left(-5\right)

10a=30

a=3

\overrightarrow{u} and \overrightarrow{v} are colinear if and only if a=3.

In which condition are \overrightarrow{u}=\dbinom{a}{20} and \overrightarrow{v}=\dbinom{\dfrac{2}{5}}{5} collinear ?

Two vectors \overrightarrow{u}=\dbinom{a}{b} and \overrightarrow{v}=\dbinom{c}{d} are collinear if and only if ad = bc. Therefore, the vectors are collinear if:

5 \times a = 20 \times \dfrac{2}{5}

5a=8

a=\dfrac{8}{5}

\overrightarrow{u} and \overrightarrow{v} are colinear if and only if a=\dfrac{8}{5}.

In which condition are \overrightarrow{u}=\dbinom{a}{9} and \overrightarrow{v}=\dbinom{4}{-\dfrac{6}{7}} collinear ?

Two vectors \overrightarrow{u}=\dbinom{a}{b} and \overrightarrow{v}=\dbinom{c}{d} are collinear if and only if ad = bc. Therefore, the vectors are collinear if:

-\dfrac{6}{7} \times a = 4 \times 9

-\dfrac{6}{7}a=36

a=-42

\overrightarrow{u} and \overrightarrow{v} are colinear if and only if a=-42.

In which condition are \overrightarrow{u}=\dbinom{a}{8} and \overrightarrow{v}=\dbinom{8}{32} collinear ?

Two vectors \overrightarrow{u}=\dbinom{a}{b} and \overrightarrow{v}=\dbinom{c}{d} are collinear if and only if ad = bc. Therefore, the vectors are collinear if:

32 \times a = 8 \times 8

32a=64

a=2

\overrightarrow{u} and \overrightarrow{v} are colinear if and only if a=2.

In which condition are \overrightarrow{u}=\dbinom{a}{12} and \overrightarrow{v}=\dbinom{-\dfrac{24}{15}}{6} collinear ?

Two vectors \overrightarrow{u}=\dbinom{a}{b} and \overrightarrow{v}=\dbinom{c}{d} are collinear if and only if ad = bc. Therefore, the vectors are collinear if:

6 \times a = 12 \times \left(-\dfrac{24}{15}\right)

6a=-\dfrac{288}{15}

a=-\dfrac{48}{15}

\overrightarrow{u} and \overrightarrow{v} are colinear if and only if a=-\dfrac{48}{15}.

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See also
  • Course : Vectors
  • Exercise : Find the components of a vector from a graph
  • Exercise : Graph a vector knowing its components
  • Exercise : Determine whether two vectors are colinear using their components
  • Exercise : Determine whether two vectors are orthogonal from their components
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