Find the area of the triangle with vertices 0 = (0,0,0), P=
(5,3,0) and Q =...
Find the area of the triangle with vertices 0 = (0,0,0), P=
(5,3,0) and Q = (6,0,5). Area=?
5. (9 pts) Find the area of the triangle with vertices at (1,
2), (5, 7),...
5. (9 pts) Find the area of the triangle with vertices at (1,
2), (5, 7), and (3, 3) u = 〈4, 5, 0〉 and v = 〈2, 1, 0〉
Find the area of the triangle with vertices:
Q(-1,-3,5), R(-2,0,7), S(-4,0,7).
Find the area of the triangle with vertices:
Q(-1,-3,5), R(-2,0,7), S(-4,0,7).
Find the area of the triangle PQR when P = (-1, 3, 1), Q = (0,...
Find the area of the triangle PQR when P = (-1, 3, 1), Q = (0,
5, 2), R = (4, 3, -1).
1. Find the area of the parallelogram that has the given vectors
as adjacent sides. Use...
1. Find the area of the parallelogram that has the given vectors
as adjacent sides. Use a computer algebra system or a graphing
utility to verify your result.
u
=
3, 2, −1
v
=
1, 2, 3
3. Find the area of the triangle with the given vertices.
Hint:
1
2
||u ✕ v||
is the area of the triangle having u and
v as adjacent
sides.
A(4, −5, 6), B(0, 1, 2), C(−1, 2, 0)
Locate ∫∫R(2x+5y)dA where R is the parallelogram with
vertices (0,0), (5,2), (4,-4), & (9,-2).
Use the...
Locate ∫∫R(2x+5y)dA where R is the parallelogram with
vertices (0,0), (5,2), (4,-4), & (9,-2).
Use the transformation x=5u+4v, y=2u−4v
1. Given the point P(5, 4, −2) and the point Q(−1, 2, 7) and
R(0, 3,...
1. Given the point P(5, 4, −2) and the point Q(−1, 2, 7) and
R(0, 3, 0) answer the following questions • What is the distance
between P and Q? • Determine the vectors P Q~ and P R~ ? • Find the
dot product between P Q~ and P R~ . • What is the angle between P
Q~ and P R~ ? • What is the projP R~ (P R~ )? • What is P Q~
1) A triangle has vertices P(–1, –5), Q(4, –11), and R(10,
–6).
Determine what type of...
1) A triangle has vertices P(–1, –5), Q(4, –11), and R(10,
–6).
Determine what type of triangle ▵PQR is.
2)A quadrilateral has vertices A(7, –2), B(9, 1), C(12, –1),
and D(10, –4).
Show that the diagonals of quadrilateral ABCD are
perpendicular to each other.
Let p = (8, 10, 3, 11, 4, 0, 5, 1, 6, 2, 7, 9) and...
Let p = (8, 10, 3, 11, 4, 0, 5, 1, 6, 2, 7, 9) and let q = (2,
4, 9, 5, 10, 6, 11, 7, 0, 8, 1, 3) be tone rows. Verify that p =
Tk(R(I(q))) for some k, and find this value of k.
Show that the quadrilateral, with vertices at A(2, 0, 5), B(0,
-3, 1), C(4, 1, -2)...
Show that the quadrilateral, with vertices at A(2, 0, 5), B(0,
-3, 1), C(4, 1, -2) and D(6, 4, 2), is a parallelogram. Calculate
the area. Determine the measures of the interior angles. Is the
parallelogram a rectangle? Verify your response.