1 thought on “A vector = 3i + 4j<br />B vector = 6i + 8j<br /><br />Find the projection of A vector along B vector ?”
Answer:
A simple diagram of the projection pp of an arbitrary vector aa onto a second arbitrary vector bb is often a good visual aid:

From trigonometry, we have the relation |p|=|a|cosθ|p|=|a|cosθ. On the other hand, the geometrical definition of the dot (or scalar, or inner) product of two vectors aa and bb is
a⋅b=|a||b|cosθ,a⋅b=|a||b|cosθ,
where θθ is the angle between the two vectors. Replacing |p|=|a|cosθ|p|=|a|cosθ in the definition yields a⋅b=|p||b|a⋅b=|p||b|, from which it follows that the magnitude (or length) of the projection is
|p|=a⋅b|b|.|p|=a⋅b|b|.
Since the projection vector pp is in the direction of bb, it must be given by
Answer:
A simple diagram of the projection pp of an arbitrary vector aa onto a second arbitrary vector bb is often a good visual aid:

From trigonometry, we have the relation |p|=|a|cosθ|p|=|a|cosθ. On the other hand, the geometrical definition of the dot (or scalar, or inner) product of two vectors aa and bb is
a⋅b=|a||b|cosθ,a⋅b=|a||b|cosθ,
where θθ is the angle between the two vectors. Replacing |p|=|a|cosθ|p|=|a|cosθ in the definition yields a⋅b=|p||b|a⋅b=|p||b|, from which it follows that the magnitude (or length) of the projection is
|p|=a⋅b|b|.|p|=a⋅b|b|.
Since the projection vector pp is in the direction of bb, it must be given by
p=|p|bˆ=|p|(b|b