64.6k views
5 votes
If a vector & b vector are perpendicular to each other, then prove (a vector + b vector) = (a vector - b vector)​

User Sadhana
by
7.8k points

1 Answer

2 votes

Final answer:

The statement that the sum and difference of two perpendicular vectors are equal is incorrect because the vectors point in different directions, and thus cannot be proved.

Step-by-step explanation:

The statement (a vector + b vector) = (a vector - b vector) is actually incorrect when vectors a and b are perpendicular to each other.

When subtracting vectors, we add the negative of the vector we're subtracting, that is A - B = A + (-B).

This applies to perpendicular vectors as well. If vectors a and b are perpendicular, their dot product is zero, meaning that they have no component in the direction of the other vector.

Thus, when we calculate a + b and a - b, we're actually getting two vectors that are perpendicular to each other, and not the same vector.

To illustrate, if a is represented by the x-axis and b by the y-axis, a + b would give us a vector going diagonally in the positive x and y direction, while a - b would result in a vector in the positive x direction and the negative y direction (essentially a reflection over the x-axis). These two will not be equal as they point in different directions.

Hence, the initial statement can't be proved because it's based on a false premise.

User Mpetla
by
7.8k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories