The vectors \(\vec A\) and \(\vec B\) are such that: \(|\vec A+\vec B| = |\vec A-\vec B|\). The angle between the two vectors is:
The vectors \(\vec A\) and \(\vec B\) are such that: \(|\vec A+\vec B| = |\vec A-\vec B|\). The angle between the two vectors is:
- 90°
- 60°
- 30°
- 0°
The Correct Option is A
Solution and Explanation
Assume that the angle between A and B is θ
The resultant of |A+B| is given by:
\(R =\sqrt {A^2 + B^2 + 2AB\ COS\ θ}\)
The resultant of |A-B| is given by:
\(R' =\sqrt {A^2 + B^2 - 2AB\ COS\ θ}\)
According to question:
\(R' = R\)
\(\sqrt {A^2 + B^2 + 2AB\ COS\ θ}\) = \(\sqrt {A^2 + B^2 - 2AB\ COS\ θ}\)
⇒ \(4AB\ COS\ θ = 0\)
⇒ \(cos\ θ = 0\),
⇒ \(θ = 90°\)
So, the correct option is (A): \(90°\)
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Concepts Used:
Multiplication of a Vector by a Scalar
When a vector is multiplied by a scalar quantity, the magnitude of the vector changes in proportion to the scalar magnitude, but the direction of the vector remains the same.
Properties of Scalar Multiplication:
The Magnitude of Vector:
In contrast, the scalar has only magnitude, and the vectors have both magnitude and direction. To determine the magnitude of a vector, we must first find the length of the vector. The magnitude of a vector formula denoted as 'v', is used to compute the length of a given vector ‘v’. So, in essence, this variable is the distance between the vector's initial point and to the endpoint.