Question

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

Answer #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|
=

Find the area of the triangle with vertices 0 = (0,0,0), P=
(5,3,0) and Q = (6,0,5). Area=?

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 =

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).

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.

Given triangle P'Q'R' and 3 parallel lines, find triangle PQR
similar to triangle P'Q'R' with one vertex on each of the given
parallel lines.

Find the area of the triangle with vertices:
Q(-1,-3,5), R(-2,0,7), S(-4,0,7).

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)=

Find the area of a triangle with vertices A (1, 4, -1), B (-1, 2,
0), C (1, 1, 3).

4)
Consider the polar curve r=e2theta
a) Find the parametric equations x = f(θ), y =
g(θ) for this curve.
b) Find the slope of the line tangent to this curve when
θ=π.
6)
a)Suppose r(t) = < cos(3t), sin(3t),4t
>.
Find the equation of the tangent line to r(t)
at the point (-1, 0, 4pi).
b) Find a vector orthogonal to the plane through the points P
(1, 1, 1), Q(2, 0, 3), and R(1, 1, 2) and the...

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