# worksheet ```Projection Vectors &amp; Work
1. Find the projection of
onto
and the vector component of
.
2. Find the vector projection of
direction of
3. Express
orthogonal to
for the vectors
and the scalar component of
in the
.
as the sum of a vector parallel to
and a vector orthogonal to
4. A woman exerts a force of 25 lb on a crate as she pushes it up a ramp that is 10 ft long and inclined at an
angle of 20&deg;. Find the work done on the box.
1. Find the scalar component of
in the direction of
if
2. Find the vector projAB if
3. Write
as the sum of a vector parallel to
and a vector orthogonal to
4. Find the scalar and vector projections of
5. Find the vector component of
orthogonal to
if
if
.
if
4. To close a sliding door on a barn, a person pulls on a rope with a constant force of 50 pounds at a constant
angle of 60 . Find the work done in moving the door 12 feet to its closed position.
5. A crate is hauled 8m up a ramp under a constant force of 200N applied at an angle of 25 to the ramp. Find
the work done.
```