Find the lengths of the sides of the triangle PQR. (a) P(4, −1,
−3), Q(8, 1,...
Find the lengths of the sides of the triangle PQR. (a) P(4, −1,
−3), Q(8, 1, 1), R(2, 3, 1)
|PQ| =
|QR| =
|RP| =
(b)
P(5, 1, −1), Q(7, 3,
0), R(7, −3, 3)
|PQ|
=
|QR|
=
|RP|
=
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.
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).
Find the area of the parallelogram PQRS with vertices P(1, 1,
0), Q(7, 1, 0), R(9,...
Find the area of the parallelogram PQRS with vertices P(1, 1,
0), Q(7, 1, 0), R(9, 4, 2), and S(3, 4, 2).
The vertices of a quadrilateral are listed below. A = (2, −3, 1)
B = (6,...
The vertices of a quadrilateral are listed below. A = (2, −3, 1)
B = (6, 5, −1) C = (7, 2, 2) D = (3, −6, 4) (a) Show that the
quadrilateral is a parallelogram. (b) Find the area of the
parallelogram.
1) Let a = 〈4,−5,−2〉 and b = 〈2,−4,−5〉 Find the projection of b
onto a....
1) Let a = 〈4,−5,−2〉 and b = 〈2,−4,−5〉 Find the projection of b
onto a. proj a b=
2) Find the area of a triangle PQR, where P=(−2,−4,0),
Q=(1,2,−1), and R=(−3,−6,5)
3) Complete the parametric equations of the line through the
points (7,6,-1) and (-4,4,8)
x(t)=7−11
y(t)=
z(t)=
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〉
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.
10.-Construct a connected bipartite graph that is not a tree
with vertices Q,R,S,T,U,V,W.
What is the...
10.-Construct a connected bipartite graph that is not a tree
with vertices Q,R,S,T,U,V,W.
What is the edge set?
Construct a bipartite graph with vertices Q,R,S,T,U,V,W such
that the degree of S is 4.
What is the edge set?
12.-Construct a simple graph with vertices F,G,H,I,J that has an
Euler trail, the degree of F is 1 and the degree of G is 3.
What is the edge set?
13.-Construct a simple graph with vertices L,M,N,O,P,Q that has
an Euler circuit...