Answered: If able please provide a visual…

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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Question

If able please provide a visual representation , this question is from linear algebra:

Let P and Q be two distinct points in space. Choose an origin O and denote the corresponding vectors as p and q. Provide a parameter representation of the line passing through P and Q in terms of p and q.

Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.

Expert Solution

Step 1: To find the vector equation of a plane:

$L e t space r with rightwards arrow on top b e space t h e space p o s i t i o n space v e c t o r space o f space a space p o i n t space o n space t h e space l i n e. A n d space l e t space lambda space b e space a space s c a l a r. T h e n space stack P Q space with rightwards arrow on top equals open parentheses q with rightwards arrow on top minus p with rightwards arrow on top close parentheses$