Question

Sketch the vectors u and w with angle θ between them and sketch the resultant.|u|=5, |w|=5, θ=45°

Answer 1

We are asked to draw a sketch of vectors "u" and "w". We have that the magnitudes of the vectors are:

`\begin{gathered} \lvert{u}\rvert=5 \\ \lvert{w}\rvert=5 \end{gathered}`

The angle between the vectors is:

`\theta=45°`

A vector is represented by an arrow whose length is the magnitude of the vector. Therefore, we need to draw two arrows with a length of 5 units and an angle between them of 45 degrees. Like this:

To determine the resultant vector we need to draw a parallel line to vector "u" from the tip of vector "w" and a parallel line to vector "w" from the tip of vector "u", like this:

Now, the resultant vector is the segment that begins from the tail of the vectors to the point where the new lines intercept, like this:

And thus we get the resultant vector.