   Chapter 12.2, Problem 16E

Chapter
Section
Textbook Problem

# Find the sum of the given vectors and illustrate geometrically.16. ⟨3, −1⟩, ⟨−1, 5⟩

To determine

To find: The sum of two vectors.

Explanation

Given:

Vectors 3,1 and 1,5 .

Definition:

Sum of vectors:

Consider the two two-dimensional vectors as a=a1,a2 and b=b1,b2 .

The vector sum of two two-dimensional vectors is,

a+b=a1+b1,a2+b2 (1)

Triangle law:

Consider two vectors u and v. Draw the vector u and second vector v at the end of vector u, then the resultant vector is sum of two vectors (u+v) .

Write the expression for vector some of vectors.

a+b=a1+b1,a2+b2

Substitute 3 for a1 , –1 for b1 , –1 for a2 , and 5 for b2 in equation (1),

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