-
Which of the following expression are
meaningful? Which are meaningless? Explain.
b, c, and d are meaningful.
-
Find the dot product of two vectors if
their lengths are and and the angle between them is
.
-
Find if , .
-
Find if and .
-
If
is a unit vector, find
and
.
From the figure, ,
and .
The angle between and is ,
and the angle between and is .
So we can write
and
-
Find the angle between vectors and
.
-
Determine whether given vectors are
orthogonal, parallel, or neither.
- , .
- , .
- ,
.
- ,
.
Neither, orthogonal, orthogonal, parallel.
-
Find two unit vectors that make an angle
of with .
-
Find the scalar and vector projections of
onto , where and .
,
.
-
Suppose that
and
are non-zero
vectors. Under what circumstances is
-
An intelligent robot exerts a horizontal
force of lb on a crate as it pushes it up a ramp that is
feet long and inclined at an angle of above
the horizontal. Find the work done on the box.
ft-lb.
-
Find the angle between a diagonal of a
cube and one of its edges.