If and ,
find and determine whether is
directed into the page or out of the page.
, into the page
If and ,
find and determine whether is
directed into the page or out of the page.
, into the page.
A bicycle is pushed by a foot with
a N force as shown. The shaft of the pedal is cm long.
Find the magnitude of the torque about .
Nm.
Let and . Find the
cross product and verify that it is orthogonal to
both and .
Find two unit vectors orthogonal to both
and .
Let , , and .
Find the vector orthogonal to the plane containing the
points , , and .
Find the area of triangle .
and ,
so .
The area is
.
A wrench cm long lies along the
positive and grips the bolt at the origin. A force is
applied in the direction at the end of the
wrench. Find the magnitude of the force needed to supply
Nm of torque to the bolt.
Approx. N.
Let be a point not on the line that passes
through the points and . Show that the distance
from the point to the line is
,
where and .
Use the formula in part (a) to find the distance from
the point to the line through the
points and .
Use cross product and dot product to find the volume of the
shape shown in the figure if , , and . If the lines look parallel,
they are.