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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
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.
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.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 4 steps
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
