Cross Product Of Parallel vectors
Cross product or vector product is the product of magnitude of the vectors with the sine of angle between the two vectors. Since parallel vector have angle 0° between them, So cross product of parallel vectors is zero.
From the definition of cross product we know,
a×b =|a| |b| sinθ Û .
Here Û represent the unit vector in the direction of a×b.
a×b = |a| |b| sin0 Û .
a×b = |a| |b| (0) Û .
a×b = 0
Hence it is proved that he cross product of two parallel vectors is always zero.
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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