Question

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| | = |

Answer #1

Find the area of the triangle PQR when P = (-1, 3, 1), Q = (0,
5, 2), R = (4, 3, -1).

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.

1. Answer the following.
a. Find the area of a triangle that has sides of lengths 9, 10
and 13 inches.
b. True or False? If a, b, and θ are two sides and an included
angle of a parallelogram, the area of the parallelogram is
absinθ.
c. Find the smallest angle (in radians) of a triangle with sides
of length 3.6,5.5,3.6,5.5, and 4.54.5 cm.
d. Given △ABC with side a=7 cm, side c=7 cm, and angle B=0.5
radians, find...

Find, correct to the nearest degree, the three angles of the
triangle with the given vertices.
P(2,
0), Q(0,
1), R(4, 3)
∠RPQ =
∠PQR =
∠QRP =

1.
Prove that the difference of the lengths of two sides of a triangle
is less than the third side.
2. Prove that in a triangle one side’s median is less than
half the sum of the other two sides.
3. Prove that the sum of the lengths of a quadrilateral’s
diagonals is less than its perimeter.

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)=

Triangle A has sides of lengths 8 cm, 12 cm and 20 cm. Triangle B
is similar to Triangle A and has a perimeter of 10 cm. What is the
length, in cm of the shortest side of Triangle B?

Find the volume of the parallelepiped with adjacent edges
PQ, PR, PS.
P(3, 0, 3), Q(−1, 2,
8), R(6, 1, 1), S(2,
6, 6)

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.

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~

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 19 minutes ago

asked 25 minutes ago

asked 26 minutes ago

asked 42 minutes ago

asked 42 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago