Question

Find a vector in the direction opposite to and with magnitude 3.

Short answer

The required vector is.

Step-by-step solution

Step 1. Given information.

The given vector is:

with magnitude 3.

Step 2. Find the norm of the vector.

Therefore, the norm of the given vector is $\sqrt{42}$.

Step 3. Find the vector.

We know that the vector in the direction of vis $\frac{a}{||\mathit{v}||}\left(\mathbf{-}\mathit{v}\right)$. Here ais the magnitude of the given vector and the negative sign shows the direction opposite to.

The required vector is:

Therefore the vector in the direction opposite toand with a magnitude of is .