Three vectors hat{i}-hat{k},lambda hat{i}+hat | vedclass

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(A) The volume $V$ of a parallelepiped with coterminous edges represented by vectors $\vec{a}$,$\vec{b}$,and $\vec{c}$ is given by the absolute value

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only $\lambda$

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(A) The volume $V$ of a parallelepiped with coterminous edges represented by vectors $\vec{a}$,$\vec{b}$,and $\vec{c}$ is given by the absolute value of the scalar triple product: $V = |\vec{a} \cdot (\vec{b} 	imes \vec{c})|$.This is equivalent to the determinant of the matrix formed by the components of the vectors:$V = |\det \begin{bmatrix} 1 & 0 & -1 \ \lambda & 1 & 1-\lambda \ \mu & \lambda & 1+\lambda-\mu \end{bmatrix}|$.Expanding the determinant along the first row:$V = |1(1(1+\lambda-\mu) - \lambda(1-\lambda)) - 0 + (-1)(\lambda(\lambda) - 1(\mu))|$.$V = |(1+\lambda-\mu - \lambda + \lambda^2) - (\lambda^2 - \mu)|$.$V = |1 + \lambda^2 - \mu - \lambda - \lambda^2 + \mu|$.$V = |1 - \lambda|$.The volume $V = |1 - \lambda|$ depends only on $\lambda$ and is independent of $\mu$.

Three vectors $\hat{i}-\hat{k}$,$\lambda \hat{i}+\hat{j}+(1-\lambda) \hat{k}$,and $\mu \hat{i}+\lambda \hat{j}+(1+\lambda-\mu) \hat{k}$ represent the coterminous edges of a parallelepiped. The volume of the parallelepiped depends on:

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