Question

Consider the points below. P(3, 3, 5), Q(-2, 5, 4), R(4, 2, 6) (a) Find a nonzero vector orthogonal to the plane through the points P, Q, and R. (1, -4, 3) (b) Find the area of the triangle PQR. 10. SCalcET8 12.4.520.XP. Find the volume of the parallelepiped determined by the vectors a, b, and c. a = ?5, 2, -3?, b = ?0, 1, 2?, c = ?4, -3, 6? cubic units

          Consider the points below.
P(3, 3, 5), Q(-2, 5, 4), R(4, 2, 6)
(a) Find a nonzero vector orthogonal to the plane through the points P, Q, and R.
(1, -4, 3)
(b) Find the area of the triangle PQR.

10. SCalcET8 12.4.520.XP.
Find the volume of the parallelepiped determined by the vectors a, b, and c.
a = ?5, 2, -3?, b = ?0, 1, 2?, c = ?4, -3, 6?
cubic units

Consider the points below.
P(3, 3, 5), Q(-2, 5, 4), R(4, 2, 6)
(a) Find a nonzero vector orthogonal to the plane through the points P, Q, and R.
(1, -4, 3)
(b) Find the area of the triangle PQR.

10. SCalcET8 12.4.520.XP.
Find the volume of the parallelepiped determined by the vectors a, b, and c.
a = ?5, 2, -3?, b = ?0, 1, 2?, c = ?4, -3, 6?
cubic units

Added by Teresa P.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

07/24/2023

Step 1

We can do this by finding the difference between the coordinates of the points: Vector PQ = Q - P = (-2 - 3, 5 - 3, 4 - 5) = (-5, 2, -1) Vector PR = R - P = (4 - 3, 2 - 3, 6 - 5) = (1, -1, 1) Now, we need to find a vector orthogonal to the plane, which can be Show more…

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Consider the points below. P(3, 3, 5), Q(-2, 5, 4), R(4, 2, 6) (a) Find a nonzero vector orthogonal to the plane through the points P, Q, and R. (1, -4, 3) (b) Find the area of the triangle PQR. 10. SCalcET8 12.4.520.XP. Find the volume of the parallelepiped determined by the vectors a, b, and c. a = ⟨5, 2, -3⟩, b = ⟨0, 1, 2⟩, c = ⟨4, -3, 6⟩ cubic units