in this practice question: Find two vectors ₁ and 2 whose sum is (5,0), where ₁ is parallel to (-4, 2) while ₂ is perpendicular to (-4,2).V1 =V2 =and

Answered: Find two vectors 1 and ₂ whose sum is…

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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Related questions

Question

in this practice question:

Find two vectors ₁ and 2 whose sum is (5,0), where ₁ is parallel to (-4, 2) while ₂ is perpendicular to (-4,2).
V1 =
V2 =
and

Expert Solution

Step 1

What is Vector:

The word "vector" is a colloquial term in mathematics and physics to refer to specific quantities that cannot be expressed by a single number or by a collection of vector space elements. Tuples, which are definite, finite sequences of numbers, are also known as vectors in some contexts. Geometric vectors and tuples may both be added to and scaled, which led to the development of the idea of a vector space, which is a set having a vector addition and a scalar multiplication that satisfies several axioms generalizing the fundamental properties of operations on the above sorts of vectors. A coordinate vector is a vector space created by tuples, whereas a Euclidean vector space is a vector space created by geometric vectors.

Given:

It is given that the sum of two vectors $\vec{v_{1}}$ and $\vec{v_{2}}$ is $<5, 0>$ . The vector $\vec{v_{1}}$ is parallel to $<- 4, 2>$ and the vector $\vec{v_{2}}$ is perpendicular to $<- 4, 2>$ .