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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 left-hand side is a linear-function of x so is the right-hand side and this means that α and β are linear scalar valued functions of x"

Please show how the left-hand 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 left-hand side is a linear-function of x so is the right-hand side and this means that α and β are linear scalar valued functions of x"

Please show how the left-hand 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..