# Vector Projections

• Nov 9th 2010, 09:07 PM
flybynight
Vector Projections
I'm given two vectors: F=9i+12j, V=3i+4j. I am asked to give the component of F parallel to V, the component of F perpendicular to V and the work done by force F through displacement V.

Any help?
Peter
• Nov 18th 2010, 09:56 AM
Unknown008
Well you can express F as:

$\vec{F} = 3(3i + 4j)$

Meaning that F is parallel to V.

Find the magnitude of F (using the Pythagoras' Theorem) this will be the parallel component.

The perpendicular component will be 0 since the two vectors are parallel.

Work Done = Force x Displacement.

Find the magnitude of the displacemnt V and you already have the force F, which is the parallel component of F to V.
• Nov 18th 2010, 10:07 AM
Plato
Quote:

Originally Posted by flybynight
I'm given two vectors: F=9i+12j, V=3i+4j. I am asked to give the component of F parallel to V, the component of F perpendicular to V and the work done by force F through displacement V.

$F_\parallel = \frac{{F \cdot V}}
{{V \cdot V}}V\;\& \,F_ \bot = F - F_\parallel
$