Answered: Vectos m and q are given, such thatt…

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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Vectos m and q are given, such thatt q=2m-22n+13p and m,n, and p are orthogonal vectors of unit length. FInd the angle between vectors and m and q

Course: Matrix Method and Linear Algebra

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

Given

q=2m-22n+13p (i)

Where m, n and p are orthogonal vectors of unit length. Then

$|m| = |n| = |p| = 1 m \cdot n = n \cdot p = m \cdot p = 0$

Now, taking dot product of (i) with m

$\begin{array}{rcl} q \cdot m & = & (2 m) \cdot m - 22 (n \cdot m) + 13 (p \cdot n) \\ = & 2 {|m|}^{2} \\ = & 2 \end{array}$

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