Sorry...I don't really understand it..MATH PROBLEM>.....?

Question

Find the component of a along b (compb a)
a=3i +5j

b=i +8 j




please answer AS COMPLETE AS POSSIBLE
because I am Stupid...
T.T


Thank You....

Answer 1

For a geometric take on what's going on, look at this figure: http://i14.tinypic.com/6p5tape.gif

Note that I've drawn a perpendicular line from the head of a to the line containing b, meeting this line in the point P. From trig, the length of line segment OP is |a| |cos(θ)|. This is the magnitude of the component of a along b. If, as in the present case, θ < 90°, then this is also the component of a along b. If θ > 90°, so that we would have to extend the line containing b beyond its tail in order to draw the perpendicular, the component of a along b is -(length of OP). Fortunately, we don't have to draw a picture in order to determine which case we have for given vectors a and b; the cos(θ) takes care of the sign.

In short, the component of a along b is

|a| cos(θ)

where |a| is the magnitude of a.

Now, recall that the dot product (a • b) is equal to
|a| |b| cos(θ). So the component of a along b is equal to

(a • b)/|b|

Since (b • b) = |b|² we can write the above as

(a • b)/sqrt(b • b)

For the given a and b, this is 43/sqrt(65)

Answer 2

Dot a with the norm of b:

{3, 5}.{1/Sqrt[1 + 64], 8/Sqrt[1 + 64]} = 5.33349
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The norm of b is the vector divided by its magnitude (Sqrt(1^2+8^2)

The dot product is the sum of the product of the i components and the product of the j components