Question

Question and answer choices are attached. Please pick the right answer and explain/show work if possible. Thanks!

Answer 1

Choice c.
`√(12)`

Explanation:

Vectors

Suppose we have a vector v defined as

`\vec v=a\mathvf{i}+b\mathvf{j}`

The magnitude of the vector is:

`\mid\mid\vec v\mid\mid=√(a^2+b^2)`

On the other hand, the dot product of the vector by itself is:

`\vec v\cdot\vec v=a*a+b*b=a^2+b^2`

Note the relation between these two operations is:

`\mid\mid\vec v\mid\mid=√(\vec v\cdot\vec v)`

Since we are given:

`\vec v\cdot\vec v=12`, then:

`\mid\mid\vec v\mid\mid=√(12)`

Choice c)
`√(12)`