P^- and Q^- are equal vectors what from the followings is true. (A) P^- and Q^- are anti paralle

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P^- and Q^- are equal vectors what from the followings is...

$\mathrm{P}^{-}$ and $\mathrm{Q}^{-}$ are equal vectors what from the followings is true. (A) $\mathrm{P}^{-}$ and $\mathrm{Q}^{-}$ are anti parallel (B) $\mathrm{P}^{-}$ and $\mathrm{Q}^{-}$ are parallel (C) $\mathrm{P}^{-}$ and $\mathrm{Q}^{-}$ may be perpendicular (D) $\mathrm{P}^{-}$ and $\mathrm{Q}^{\rightarrow}$ may be free vectors

$\mathrm{P}^{-}$ and $\mathrm{Q}^{-}$ are equal vectors what from the followings is true.
(A) $\mathrm{P}^{-}$ and $\mathrm{Q}^{-}$ are anti parallel
(B) $\mathrm{P}^{-}$ and $\mathrm{Q}^{-}$ are parallel
(C) $\mathrm{P}^{-}$ and $\mathrm{Q}^{-}$ may be perpendicular
(D) $\mathrm{P}^{-}$ and $\mathrm{Q}^{\rightarrow}$ may be free vectors

Key Concepts

Free Vectors

Free vectors are those whose properties, such as magnitude and direction, are independent of their position; they can be freely moved in space without changing their characteristics. This concept is useful in physics and mathematics, as it allows the idea that vectors can be compared and added based solely on their direction and magnitude.

Perpendicular Vectors

Perpendicular vectors are vectors that intersect at a right angle (90 degrees) to each other. If two vectors are equal (sharing both magnitude and direction), they cannot be perpendicular as this would require a 90-degree difference in direction.

Vector Equality

Vector equality means that two vectors have the same magnitude and direction independently of their initial points. This concept is fundamental in linear algebra and physics because it emphasizes that vectors are defined solely by their magnitude and direction rather than their location in space.

Parallel Vectors

Parallel vectors are vectors that have the same or exactly opposite direction; in other words, they lie along the same line. When two vectors are equal, they necessarily point in the same direction, making them a specific case of parallel vectors.

Anti-parallel Vectors

Anti-parallel vectors are a subtype of parallel vectors where the two vectors have the same magnitude but point in opposite directions. Although they are collinear, they are not equal because their directions differ by 180 degrees.

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