Scalar Product/Dot Product of Vectors
The resultant scalar product/dot product of two vectors is always a scalar quantity. Consider two vectors a and b. The scalar product is calculated as the product of magnitudes of a, b, and cosine of the angle between these vectors.
Scalar Product = |a||b| cos α
Here,
- |a| = magnitude of vector a,
- |b| = magnitude of vector b, and
- α = angle between the vectors.
Projection of one vector on other Vector
Vector a can be projected on the line l as shown below:
It is clear from the above figure that we can project one vector over another vector. AC is the magnitude of vector A. In the above figure, AD is drawn perpendicular to line l. CD represents the projection of vector a on vector b.
Triangle ACD is thus a right-angled triangle, and we can apply trigonometric formulae.
If α is the measure of angle ACD, then
cos α = CD/AC
Or, CD = AC cos α
From the figure, it is clear that CD is the projection of vector a on vector b
So, we can conclude that one vector can be projected over the other vector by the cosine of the angle between them.
Dot and Cross Products on Vectors
A quantity that is characterized not only by magnitude but also by its direction, is called a vector. Velocity, force, acceleration, momentum, etc. are vectors.
Vectors can be multiplied in two ways:
- Scalar product or Dot product
- Vector Product or Cross product
Table of Content
- Scalar Product/Dot Product of Vectors
- Projection of one vector on other Vector
- Properties of Scalar Product
- Inequalities Based on Dot Product
- Cross Product/Vector Product of Vectors
- Properties of Cross Product
- Cross product in Determinant Form
- Dot and Cross Product
- FAQs on Dot and Cross Products on Vectors
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