# Simple Vector Component Projection

## Homework Statement

Consider the two vectors A=ai and B=3i+4j. What must be the value of a if the component of A along B is 6?

## The Attempt at a Solution

I've arrived at the correct answer by finding the angle between the x component of B (3) and B itself which comes out to 53.13 degrees. Then 6/cos53.13 = 10 which is the correct result. However, I still don't understand what it means for something to be the component of A along B. I was hoping someone here could shed some light on what this means and how to visualize it.

Thank you,
Odd

Hootenanny
Staff Emeritus
Gold Member
BruceW
Homework Helper
Hootenanny, do you mean scalar product? If so, then yeah, I agree. The sentence 'component of A along B' is simply the scalar product of the vectors A and the unit vector of B, ie B/ lBl.

The scalar product can be written out in terms of the components of the two vectors as: (A1B1+A2B2+A3B3) / lBl (when the vectors are expressed in some orthogonal coordinate system).

For a geometrical representation, the scalar product of A and the unit vector B / lBl is also equal to lAl cos(angle) where angle is the angle between those vectors.

The intuitive way to think of 'the component of A along B' is that you simply look at the length of the vector A in the same direction as B.

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