If A⃗ and B⃗ are vectors and B⃗=-A⃗, which of the following is true? a) The magnitude of B⃗ is e

step 1 If A and B are two vectors and vector B is equal to the negative of vector A, which are the foll

If A⃗ and B⃗ are vectors and B⃗=-A⃗, which of the following...

If $\vec{A}$ and $\vec{B}$ are vectors and $\vec{B}=-\vec{A},$ which of the following is true? a) The magnitude of $\vec{B}$ is equal to the negative of the magnitude of $\vec{A}$. b) $\vec{A}$ and $\vec{B}$ are perpendicular. c) The direction angle of $\vec{B}$ is equal to the direction angle of $\vec{A}$ plus $180^{\circ}$ d) $\vec{A}+\vec{B}=2 \vec{A}$.

If $\vec{A}$ and $\vec{B}$ are vectors and $\vec{B}=-\vec{A},$ which of the following is true?
a) The magnitude of $\vec{B}$ is equal to the negative of the magnitude of $\vec{A}$.
b) $\vec{A}$ and $\vec{B}$ are perpendicular.
c) The direction angle of $\vec{B}$ is equal to the direction angle of $\vec{A}$ plus $180^{\circ}$
d) $\vec{A}+\vec{B}=2 \vec{A}$.

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Key Concepts

Vector Addition

Vector addition involves combining two or more vectors to form a resultant vector, usually by adding corresponding components. When a vector is added to its negation, the result is the zero vector, demonstrating the inverse relationship that exists between a vector and its negative.

Vector Negation

Vector negation is the concept where a vector is multiplied by -1, which reverses its direction while keeping its magnitude unchanged. This operation is fundamental in vector algebra and is key to understanding relationships such as how two opposite vectors are related.

Magnitude of a Vector

The magnitude of a vector, often represented as its length or norm, measures its size without considering its direction. It is always a non-negative value, and when a vector is negated, its magnitude remains the same, emphasizing that magnitude is independent of direction.

Direction Angle

The direction angle of a vector is the angle between the vector and a reference axis, typically the positive x-axis. When a vector is negated, its direction is rotated by 180° from the original, which is important for understanding how vector direction changes under negation.

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