Vectors

[Fudge111211111]

I Don’t know how to get the answer for these 3 questions. Guidance needed please

 

[Dr.Peterson]

Let's focus on (a)(i). Draw a figure with just O, A, and B, and with arrows showing OA, OB, and AB. Look to see if any two of these add up to the other (that is, they go head to tail). Write an equation that expresses that sum, and solve for AB. (With experience, you would be able to write the answer immediately, but not yet!)

For the other parts, you are probably expected to use some knowledge of which parts of a regular hexagon are parallel or congruent, but we'll get there.

 

[Fudge111211111]

Let's focus on (a)(i). Draw a figure with just O, A, and B, and with arrows showing OA, OB, and AB. Look to see if any two of these add up to the other (that is, they go head to tail). Write an equation that expresses that sum, and solve for AB. (With experience, you would be able to write the answer immediately, but not yet!)

For the other parts, you are probably expected to use some knowledge of which parts of a regular hexagon are parallel or congruent, but we'll get there.

I understand how to do to the first question- it’s 6b-6a
It’s the other 2 which I do not know how to do

 

[Dr.Peterson]

Ok. What does the fact that this is a regular hexagon tell you about side EF? (Ignore vectors for the moment, unless you see something to say about them.)

Then for (b), what can you say about BC?And how is BX related to BC?

The general idea of problem solving is to first take inventory of what you do know that might be of use. That may be enough to make you aware of steps you can take.

 

[pka]

View attachment 16821
I Don’t know how to get the answer for these 3 questions. Guidance needed please

To Fudge111211111, This appears to be from the same source as the question on combinatorics. If I were you I would find myself a more up-to-date set of questions. As to the above vector question, there is not one standard bit of notation about it. You are not preparing yourself for real university study by using faulty material.
That said, we can use the properties of a regular hexagon to see that points \(E,~O,~\&~B\) are collinear. Moreover, \(\overrightarrow {EO} = \overrightarrow {OB} \)
That last equality will be challenged. But we have to realize that vectors are not mathematical objects, i.e. a set, they are equivalence classes of objects that have the same direction and length. Thus \(\overrightarrow {EX} = 2\overrightarrow {OB} + 0.5\overrightarrow {BC} \)