 #1
 106
 4
Dear all, I am trying to understand the vector triple product.
## x\times (y \times z) ##
As the vector triple product of x,y and z lies in the plane ## (y \times z) ## the vector ## x\times (y \times z) ## can be written as a linear combination of the vectors ## \pm y ## & ## \pm z##
In the passage attached, can anyone please explain this " As the lefthand side is a linearfunction of x so is the righthand side and this means that α and β are linear scalar valued functions of x"
Please show how the lefthand side is a linear function of x. What does linearity in vectors mean? Can anyone please explain in a bit of detail.
Also, what does Linear scalar valuesd functions of x mean? Please explain Theorem 4.2.5. To my understanding, this function changes a vector into a scalar. What does it mean to say ## f : ℝ^3 → ℝ ## is linear. Please give examples.
Danke..
## x\times (y \times z) ##
As the vector triple product of x,y and z lies in the plane ## (y \times z) ## the vector ## x\times (y \times z) ## can be written as a linear combination of the vectors ## \pm y ## & ## \pm z##
In the passage attached, can anyone please explain this " As the lefthand side is a linearfunction of x so is the righthand side and this means that α and β are linear scalar valued functions of x"
Please show how the lefthand side is a linear function of x. What does linearity in vectors mean? Can anyone please explain in a bit of detail.
Also, what does Linear scalar valuesd functions of x mean? Please explain Theorem 4.2.5. To my understanding, this function changes a vector into a scalar. What does it mean to say ## f : ℝ^3 → ℝ ## is linear. Please give examples.
Danke..
Attachments

80.8 KB Views: 406