Two vectors A and B are such that ∣→A + →B∣ = ∣→A − →B∣ then what is the angle between →A and →B :-

• A 90°
• B 60°
• C 75°
• D 45°

To find the angle between the vectors A and B given that ∣→A + →B∣ = ∣→A − →B∣, we can use the properties of vectors and the cosine rule.

Understanding the Condition

The condition states that the magnitudes of the sum and difference of the vectors are equal. This can be expressed mathematically as:

∣→A + →B∣² = ∣→A − →B∣²

Expanding Both Sides

Using the formula for the magnitude of vectors, we expand both sides:

• ∣→A + →B∣² = ∣→A∣² + ∣→B∣² + 2(→A • →B)
• ∣→A − →B∣² = ∣→A∣² + ∣→B∣² - 2(→A • →B)

Setting the Equations Equal

Setting these two expansions equal gives:

∣→A∣² + ∣→B∣² + 2(→A • →B) = ∣→A∣² + ∣→B∣² - 2(→A • →B)

Simplifying the Equation

By simplifying, we find:

4(→A • →B) = 0

This implies that:

→A • →B = 0

Interpreting the Result

The dot product of two vectors is zero when the vectors are perpendicular to each other. Therefore, the angle θ between the vectors A and B is:

θ = 90°

Final Answer

The angle between vectors A and B is 90°.