Equal Vectors

In this publication, we will consider which vectors are called equal and how to determine their equality. We will also analyze examples of tasks on this topic.

Condition of equality of vectors

Vectors a и b are equal if they have the same , they lie on the same or parallel lines, and also point to the same side. That is, such vectors are collinear, co-directed and equal in length.

a = b, if a ↑↑ b and |a| = |b|.

Note: vectors are equal if their coordinates are equal.

Examples of tasks

Task 1

Which of the vectors are equal: a = {6; 8}, b = {-2; 5} и c = {6; 8}.

Decision:

Of the listed vectors are equal a и c, since they have the same coordinates:

a_x = c_x = 6

a_y = c_y = 8.

Task 2

Let us find out for what value n vectors a = {1; 18; 10} и b = {1; 3n; 10} are equal.

Decision:

First, check the equality of known coordinates:

a_x = b_x = 1

a_z = b_z = 10

For equality to be true, it is necessary that a_y = b_y:

3n = 18, hence n = 6.