Vector Question A level Maths

Hi,
Could someone please help me with the second part of this question.
I don't understand how to use the diagram for the question.
The markscheme says '3i + 4j and 5i shown on diagram'.
How would this look like on the diagram? How does this help me find the value for k?

Value of k determines how long the b arrow is.

If you join the tail of a arrow to the head of b arrow, and create a new arrow (i.e. vector), then the length of this will be equivalent to |a + kb|.

As |a + kb| = 5 then this new line should be of length 5 ... so if you image this as a hypotenuse of a right-angle then the other two lengths can be 3,4 (this is not obvious if you are not familiar with the 3,4,5 right triangle).

So the idea is as follows: how long should the b arrow be so that your new line creates a 3,4,5 triangle? Solution is attached below.

Clearly, we end up taking HALF of the vector b ... so k = 1/2

There is another k value.

The easy way to see what these two are is to draw a circle of radius 5 about the tail of a arrow and see where the b arrow intersects it.