Answer:
[tex]a)\ \overrightarrow{FB}=5b\\\\b)\ \overrightarrow{FD}=5b-2a\\\\c)\ \overrightarrow{CB}=2a-5b[/tex]
Step-by-step explanation:
You want the vectors FB, FD, and CB given those shown in the diagram.
(a) Vector
A vector is a directed line segment. It is named by naming its tail first, then its head. This is reinforced by the arrow over the vector's name.
If we assume all the triangles in the figure that look congruent are congruent, then any of the parallel (left-to-right) horizontal short segments are fully equivalent to the one labeled "5b". This means ...
vector FB = 5b
All of the short segments in the upper-right direction are equivalent to the one labeled "2a".
(b, c) Differences
The vector that joins the heads of two vectors (that originate from the same point) is the difference between the vector to the head and the vector to the tail. This means ...
vector FD = 5b -2a
The vector CB is in the opposite direction. It will be the negative of the parallel vector FD. Or, you can think of CB as the difference between vectors DB and DC.
vector CB = 2a -5b
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Additional comment
Vectors are the 2- or 3-dimensional equivalent of segments on a number line. As you know, you can add numbers on a number line by putting their lengths "nose-to-tail". Positive numbers have a direction to the right, and negative numbers have a direction to the left.
On a number line, a number is subtracted by adding its opposite. That is, the sum 6 -2 would start from the origin with moving 6 units to the right. Then the subtraction of 2 would be accomplished by adding -2, which is a distance of 2 to the left.
Vectors work the same way, but their direction is not limited to left or right. The vector FD in the figure is parallel to, and the same length as, the one that you get when you add -2a to 5b. That is, if you translate segment FE (vector -2a) so that F' lands on top of D, then the vector EE' is parallel to FD and its same length. This gives you EE' as the sum 5b-2a.
Did you take advantage of the "Watch video" button? It may be able to explain all of this better than I can.
