Question

2. Consider the points in xyz-space A = (-2, 3, 0) B = (-1, 7, -2) C = (-2, 8, -3). (a) Find vector that is perpendicular to both AB and AC. (b) What is the area of the triangle with vertices A, B, and C? (c) Find the Cartesian equation ax + by + cz = d of the plane that passes through A, B, and C. (d) What is the shortest distance from the plane that passes through A, B, and C, and the plane described by the Cartesian equation 2x - 3y - 5z = 0? [5+2+2+2 = 11 marks]

          2. Consider the points in xyz-space
A = (-2, 3, 0) B = (-1, 7, -2) C = (-2, 8, -3).
(a) Find vector that is perpendicular to both AB and AC.
(b) What is the area of the triangle with vertices A, B, and C?
(c) Find the Cartesian equation ax + by + cz = d of the plane that passes through A, B, and C.
(d) What is the shortest distance from the plane that passes through A, B, and C, and the plane described by the Cartesian equation 2x - 3y - 5z = 0?
[5+2+2+2 = 11 marks]

2. Consider the points in xyz-space
A = (-2, 3, 0) B = (-1, 7, -2) C = (-2, 8, -3).
(a) Find vector that is perpendicular to both AB and AC.
(b) What is the area of the triangle with vertices A, B, and C?
(c) Find the Cartesian equation ax + by + cz = d of the plane that passes through A, B, and C.
(d) What is the shortest distance from the plane that passes through A, B, and C, and the plane described by the Cartesian equation 2x - 3y - 5z = 0?
[5+2+2+2 = 11 marks]

Added by Jenny R.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Ben Blakesley

Step 1

Find the vector AB and AC. AB = B - A = (-1 - (-2), 7 - 3, -2 - 0) = (1, 4, -2) AC = C - A = (-2 - (-2), 8 - 3, -3 - 0) = (0, 5, -3) Show more…

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Consider the points in xyz-space A = (-2, 3, 0) B = (-1, 7, -2) C = (-2, 8, -3). (a) Find vector that is perpendicular to both AB and AC. (b) What is the area of the triangle with vertices A, B, and C? (c) Find the Cartesian equation ax + by + cz = d of the plane that passes through A, B, and C. (d) What is the shortest distance from the plane that passes through A, B, and C, and the plane described by the Cartesian equation 2x - 3y - 5z = 0? [5+2+2+2 = 11 marks]