Answer:
Choice c. [tex]\sqrt{12}[/tex]
Step-by-step explanation:
Vectors
Suppose we have a vector v defined as
[tex]\vec v=a\mathvf{i}+b\mathvf{j}[/tex]
The magnitude of the vector is:
[tex]\mid\mid\vec v\mid\mid=\sqrt{a^2+b^2}[/tex]
On the other hand, the dot product of the vector by itself is:
[tex]\vec v\cdot\vec v=a*a+b*b=a^2+b^2[/tex]
Note the relation between these two operations is:
[tex]\mid\mid\vec v\mid\mid=\sqrt{\vec v\cdot\vec v}[/tex]
Since we are given:
[tex]\vec v\cdot\vec v=12[/tex], then:
[tex]\mid\mid\vec v\mid\mid=\sqrt{12}[/tex]
Choice c) [tex]\sqrt{12}[/tex]
