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Suppose you have a box centred at C(a, b, a + b), having a length (along x-axis) of 2a units, width (along y-axis) 4b units and height (along z-axis) of 8(a + b) units. Using dot and cross products, illustrate whether the point P(4a², b², 16ab) lies inside or outside of the box.

Suppose you have a box centred at C(a, b, a + b), having a length (along x-axis) of 2a units, width (along y-axis) 4b units and height (along z-axis) of 8(a + b) units. Using dot and cross products, illustrate whether the point P(4a², b², 16ab) lies inside or outside of the box.

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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DOT AND CROSS PRODUCT ARE A MUST to determine whether the chosen point lies within or outside the box.

Dot product of vectors: Defined as ||v1|| * ||v2|| = ||v1||||v2||cosΘ, where Θ is the angle between v1 and v2. Or, v1*v2 = v1x*v2x + v1y * v2y

Cross Product of Vectors: axb = a * b * sinΘn

a = 5

b = 2

Illustrate the coordinates of each corner of the box, and specify whether the point P is in front or behind each face of the box.

2. Suppose you have a box centred at C(a, b, a + b), having a length (along x-axis) of 2a units, width (along y-axis) 4b units and height (along z-axis) of 8(a + b) units. Using dot and cross products, illustrate whether the point P(4a², ¹b², 16ab) lies inside or outside of the box.
Transcribed Image Text:2. Suppose you have a box centred at C(a, b, a + b), having a length (along x-axis) of 2a units, width (along y-axis) 4b units and height (along z-axis) of 8(a + b) units. Using dot and cross products, illustrate whether the point P(4a², ¹b², 16ab) lies inside or outside of the box.
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