mail
mail@stemandmusic.in
call
+91-9818088802
Donate
Scalar Quad Product
The
Scalar Quad Product
of 4
3-Dimensional Vectors
\(\vec{A}\), \(\vec{B}\), \(\vec{C}\) and \(\vec{D}\) is calculated as follows
\((\vec{A} \times \vec{B}) \cdot (\vec{C} \times \vec{D})=\begin{vmatrix} \vec{A}\cdot\vec{C} & \vec{A}\cdot\vec{D} \\\vec{B}\cdot\vec{C} & \vec{B}\cdot\vec{D}\end{vmatrix} =(\vec{A}\cdot\vec{C})(\vec{B}\cdot\vec{D})-(\vec{A}\cdot\vec{D})(\vec{B}\cdot\vec{C})\)
The
Scalar Quad Product
can be used to calculate
Square of the Magnitude of the
Cross Product
Between 2 Vectors \(\vec{A}\) and \(\vec{B}\)
as follows
\(|\vec{A} \times \vec{B}|^2=(\vec{A} \times \vec{B}) \cdot (\vec{A} \times \vec{B})=(\vec{A}\cdot\vec{A})(\vec{B}\cdot\vec{B})-{(\vec{A}\cdot\vec{B})}^2\)
Please note that this is same as calculating the
Determinant of Metric Tensor
of a Matrix containing Vectors \(\vec{A}\) and \(\vec{B}\) as it's Columns
.
Related Topics
Scalar Triple Product
,
Vector Triple Product
,
Vector Quad Product
,
Introduction to Vector Algebra
Home
|
TOC
|
Calculators
©
Invincible IDeAS
. All Rights Reserved