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2. Let p₁ = (2,-1,8), p2 = =(5, -3,9) and p3 = (0, -1, 14) (a) Show that the three points define a right triangle. Hint: The difference between two vertices in a vector whose direction coincides with that of a triangle side, and a pair of such vectors must be orthogonal in order for the triangle to be a right triangle. (b) Specify a vector N that is normal to the plane of P1, P2, P3. Hint: Ñ must be orthogonal to P2P1, P3 P2, P1 P2 and can be computed with a vector cross product. (c) Specify the area of the triangle defined by P1, P2, P3.

2. Let p₁ = (2,-1,8), p2 = =(5, -3,9) and p3 = (0, -1, 14) (a) Show that the three points define a right triangle. Hint: The difference between two vertices in a vector whose direction coincides with that of a triangle side, and a pair of such vectors must be orthogonal in order for the triangle to be a right triangle. (b) Specify a vector N that is normal to the plane of P1, P2, P3. Hint: Ñ must be orthogonal to P2P1, P3 P2, P1 P2 and can be computed with a vector cross product. (c) Specify the area of the triangle defined by P1, P2, P3.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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2. Let p₁ = (2,-1,8), p2 = (5,-3,9) and p3 = (0, -1, 14) (a) Show that the three points define a right triangle. Hint: The difference between two vertices in a vector whose direction coincides with that of a triangle side, and a pair of such vectors must be orthogonal in order for the triangle to be a right triangle. (b) Specify a vector Ñ that is normal to the plane of P1, P2, P3. Hint: Ñ must be orthogonal to P2P1, P3 P2, P1 P2 and can be computed with a vector cross product. (c) Specify the area of the triangle defined by P1, P2, P3. (d) Specify the condition that p = (x, y, z) lies in the plane of P1, P2, P3 (as an equation in x, y, and z). Recall that the equation of a plane has the form Ax+By+Cz+ D = 0.
Transcribed Image Text:2. Let p₁ = (2,-1,8), p2 = (5,-3,9) and p3 = (0, -1, 14) (a) Show that the three points define a right triangle. Hint: The difference between two vertices in a vector whose direction coincides with that of a triangle side, and a pair of such vectors must be orthogonal in order for the triangle to be a right triangle. (b) Specify a vector Ñ that is normal to the plane of P1, P2, P3. Hint: Ñ must be orthogonal to P2P1, P3 P2, P1 P2 and can be computed with a vector cross product. (c) Specify the area of the triangle defined by P1, P2, P3. (d) Specify the condition that p = (x, y, z) lies in the plane of P1, P2, P3 (as an equation in x, y, and z). Recall that the equation of a plane has the form Ax+By+Cz+ D = 0.
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