(a) To find: The vector perpendicular to the plane passing through the three points, P ( 1 , 0 , 0 ) , Q ( 2 , 0 , − 1 ) and R ( 1 , 4 , 3 ) .

Question

Find the perimeter and area

Answer 1

Question

Chapter 9.CT, Problem 10CT

To determine

(a)

To find:

The vector perpendicular to the plane passing through the three points, P(1,0,0), Q(2,0,−1) and R(1,4,3).

To determine

(b)

To find:

The equation of the plane that passes through the points P, Q, and R.

To determine

(c)

To find:

The area of the triangle PQR.

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Find the perimeter and area

Assume {u1, U2, us} spans R³. Select the best statement. A. {U1, U2, us, u4} spans R³ unless u is the zero vector. B. {U1, U2, us, u4} always spans R³. C. {U1, U2, us, u4} spans R³ unless u is a scalar multiple of another vector in the set. D. We do not have sufficient information to determine if {u₁, u2, 43, 114} spans R³. OE. {U1, U2, 3, 4} never spans R³. F. none of the above

Assume {u1, U2, 13, 14} spans R³. Select the best statement. A. {U1, U2, u3} never spans R³ since it is a proper subset of a spanning set. B. {U1, U2, u3} spans R³ unless one of the vectors is the zero vector. C. {u1, U2, us} spans R³ unless one of the vectors is a scalar multiple of another vector in the set. D. {U1, U2, us} always spans R³. E. {U1, U2, u3} may, but does not have to, span R³. F. none of the above

Answer 2

Question

Chapter 9.CT, Problem 10CT

To determine

(a)

To find:

The vector perpendicular to the plane passing through the three points, P(1,0,0), Q(2,0,−1) and R(1,4,3).

To determine

(b)

To find:

The equation of the plane that passes through the points P, Q, and R.

To determine

(c)

To find:

The area of the triangle PQR.

Expert Solution & Answer

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Answer 3

Question

Chapter 9.CT, Problem 10CT

To determine

(a)

To find:

The vector perpendicular to the plane passing through the three points, P(1,0,0), Q(2,0,−1) and R(1,4,3).

To determine

(b)

To find:

The equation of the plane that passes through the points P, Q, and R.

To determine

(c)

To find:

The area of the triangle PQR.

Expert Solution & Answer

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Answer 4

Question

Chapter 9.CT, Problem 10CT

To determine

(a)

To find:

The vector perpendicular to the plane passing through the three points, P(1,0,0), Q(2,0,−1) and R(1,4,3).

To determine

(b)

To find:

The equation of the plane that passes through the points P, Q, and R.

To determine

(c)

To find:

The area of the triangle PQR.

Expert Solution & Answer

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Answer 5

Chapter 9.CT, Problem 10CT

To determine

(a)

To find:

The vector perpendicular to the plane passing through the three points, P(1,0,0), Q(2,0,−1) and R(1,4,3).

To determine

(b)

To find:

The equation of the plane that passes through the points P, Q, and R.

To determine

(c)

To find:

The area of the triangle PQR.

Answer 6

Chapter 9.CT, Problem 10CT

To determine

(a)

To find:

The vector perpendicular to the plane passing through the three points, P(1,0,0), Q(2,0,−1) and R(1,4,3).

Answer 7

Chapter 9.CT, Problem 10CT

To determine

(a)

To find:

The vector perpendicular to the plane passing through the three points, P(1,0,0), Q(2,0,−1) and R(1,4,3).

Answer 8

To determine

(b)

To find:

The equation of the plane that passes through the points P, Q, and R.

Answer 9

To determine

(b)

To find:

The equation of the plane that passes through the points P, Q, and R.

Answer 10

To determine

(c)

To find:

The area of the triangle PQR.

Answer 11

To determine

(c)

To find:

The area of the triangle PQR.

Answer 12

Expert Solution & Answer

Answer 13

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Answer 23

Ch. 9.1 - Prob. 1E Ch. 9.1 - CONCEPTS 2. a The length of a vector w=a1,a2 is...Ch. 9.1 - 38 Sketching Vectors Sketch the vector indicated....Ch. 9.1 - Prob. 4E Ch. 9.1 - Prob. 5E Ch. 9.1 - Prob. 6E Ch. 9.1 - SKILLS 3-8 Sketching Vectors Sketch the vector...Ch. 9.1 - Prob. 8E Ch. 9.1 - Prob. 9E Ch. 9.1 - Prob. 10E

(a) To find: The vector perpendicular to the plane passing through the three points, P ( 1 , 0 , 0 ) , Q ( 2 , 0 , − 1 ) and R ( 1 , 4 , 3 ) .

Solution Summary: The author calculates that the vector perpendicular to the plane passing through the three points is 4i-3j+4k.

Concept explainers

Videos

(a)

To find:

The vector perpendicular to the plane passing through the three points, P(1,0,0), Q(2,0,−1) and R(1,4,3).

(b)

To find:

The equation of the plane that passes through the points P, Q, and R.

(c)

To find:

The area of the triangle PQR.

Chapter 9 Solutions

(a) To find: The vector perpendicular to the plane passing through the three points, P ( 1 , 0 , 0 ) , Q ( 2 , 0 , − 1 ) and R ( 1 , 4 , 3 ) .

Solution Summary: The author calculates that the vector perpendicular to the plane passing through the three points is 4i-3j+4k.

Concept explainers

Videos

(a) To find: The vector perpendicular to the plane passing through the three points, P(1,0,0), Q(2,0,−1) and R(1,4,3).

(b) To find: The equation of the plane that passes through the points P, Q, and R.

(c) To find: The area of the triangle PQR.

Chapter 9 Solutions

(a)

To find:

The vector perpendicular to the plane passing through the three points, P(1,0,0), Q(2,0,−1) and R(1,4,3).

(b)

To find:

The equation of the plane that passes through the points P, Q, and R.

(c)

To find:

The area of the triangle PQR.