When two vectors are multiplied with each other and the answer is a scalar quantity then such a product is called the scalar product or dot product of vectors.
A dot (.) is placed between vectors which are multiplied with each other that’s why it is also called “dot product”.
Scalar = vector .vector
i.e W =F . S
i.e P =F . V
i.e Φ = E . A
The product of magnitudes of vectors and the cosine of an angle between them. Consider two vectors A and B making an angle θ with each other.
A . B = AB Cos θ
Where “B Cos θ ” is the component of B along with vector A and 0 ≤ θ ≤ π.
i.e A . B = AB Cos 0º=AB (1) =AB
A . A = AA Cos 0º=A² (1)=A²
i.e A . B = AB Cos 180º=AB (-1) = -AB
i.e A . B = AB Cos 90º=AB (0) = 0
i.e i. i = j . j = k . k = 1
and
i. j = j . k = k . i = 0
“When two vectors are multiplied with each other and the answer is also a vector quantity then such a product is called vector cross product or vector product.”
A cross (×) is placed between the vectors which are multiplied with each other that’s why it is also known as “cross product”.i.e
Vector = Vector × Vector
i.e τ = r × F
i.e V t = ω × r
The cross product is defined by the relation
C = A × B = AB Sinθ u
Where u is a unit vector perpendicular to both A and B.
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Sir dot m costhita hi q sinthita q nhi
nice answers.
yah i got good answers that makes me to understand