Are \overrightarrow{u}=\dbinom{3}{2} and \overrightarrow{v}=\dbinom{6}{3} collinear ?
Two vectors \overrightarrow{u}=\dbinom{a}{b} and \overrightarrow{v}=\dbinom{c}{d} are collinear if and only if:
ad = bc
Here, we have:
- ad = 3 \times 3 =9
- bc= 2 \times 6 = 12
Therefore:
ad \ne bc
The vectors are not collinear.
Are \overrightarrow{u}=\dbinom{3}{2} and \overrightarrow{v}=\dbinom{6}{4} collinear ?
Two vectors \overrightarrow{u}=\dbinom{a}{b} and \overrightarrow{v}=\dbinom{c}{d} are collinear if and only if:
ad = bc
Here, we have:
- ad = 3 \times4=12
- bc= 6 \times2= 12
Therefore:
ad= bc
The vectors are collinear.
Are \overrightarrow{u}=\dbinom{2}{0} and \overrightarrow{v}=\dbinom{8}{0} collinear ?
Two vectors \overrightarrow{u}=\dbinom{a}{b} and \overrightarrow{v}=\dbinom{c}{d} are collinear if and only if:
ad = bc
Here, we have:
- ad = 2 \times 0 =0
- bc= 8 \times0 = 0
Therefore:
ad = bc
The vectors are collinear.
Are \overrightarrow{u}=\dbinom{2}{-1} and \overrightarrow{v}=\dbinom{5}{4} collinear ?
Two vectors \overrightarrow{u}=\dbinom{a}{b} and \overrightarrow{v}=\dbinom{c}{d} are collinear if and only if:
ad = bc
Here, we have:
- ad = 2 \times 4 =8
- bc= 5 \times-1 = -5
Therefore:
ad \ne bc
The vectors are not collinear.
Are \overrightarrow{u}=\dbinom{4}{-2} and \overrightarrow{v}=\dbinom{3}{7} collinear ?
Two vectors \overrightarrow{u}=\dbinom{a}{b} and \overrightarrow{v}=\dbinom{c}{d} are collinear if and only if:
ad = bc
Here, we have:
- ad = 4 \times 7 =28
- bc= -2 \times 3 = -6
Therefore:
ad \ne bc
The vectors are not collinear.
Are \overrightarrow{u}=\dbinom{5}{2} and \overrightarrow{v}=\dbinom{10}{4} collinear ?
Two vectors \overrightarrow{u}=\dbinom{a}{b} and \overrightarrow{v}=\dbinom{c}{d} are collinear if and only if:
ad = bc
Here, we have:
- ad = 5 \times 4 =20
- bc= 2 \times 10 = 20
Therefore:
ad= bc
The vectors are collinear.
Are \overrightarrow{u}=\dbinom{1}{-1} and \overrightarrow{v}=\dbinom{2}{-4} collinear ?
Two vectors \overrightarrow{u}=\dbinom{a}{b} and \overrightarrow{v}=\dbinom{c}{d} are collinear if and only if:
ad = bc
Here, we have:
- ad = 1 \times -4 =-4
- bc= 2 \times -1 = -2
Therefore:
ad \ne bc
The vectors are not collinear.