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}.