FAQ on Parallel Vector
What are parallel vectors?
Parallel vectors are vectors that always have the same or opposite directions but can have different magnitudes.
Can parallel vectors be called collinear vectors?
Yes, parallel vectors can be called collinear vectors when they lie along the same line or when they can be represented by the same line.
Do parallel vectors always have the same starting and ending points?
No, parallel vectors do not need to start and end at the same point. They can have different starting and ending points, such as 3i and 8i, which are parallel to each other.
Is there any vector parallel to every other vector?
Yes, the zero vector (with each part being zero, i.e., 0i + 0j + 0k) is considered parallel to every other vector.
Why is every vector parallel to itself?
Every vector is parallel to itself because every vector can be written as a scalar multiple of itself, e.g., a = 1×a.
Are parallel vectors and equal vectors the same?
No, parallel vectors and equal vectors are two different entities. Equal vectors always have the same magnitude and direction, whereas parallel vectors may or may not have equal magnitudes and can be in the same or opposite directions.
Parallel Vector
Parallel vectors are considered one of the most important concepts in vector algebra. When two vectors have the same or opposite direction, they are said to be parallel to each other. Note that parallel vectors can differ in magnitude, and two parallel vectors can never intersect each other. They are widely used in mathematics, physics, and other areas of engineering for defining lines and planes, representing force and velocity, and analyzing various structures.
In this article, we will learn about parallel vectors, the dot product, and the cross product of parallel vectors, as well as their properties, in detail.
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