91Ó°ÊÓ

In Exercises 55-58, use the triple scalar product to find the volume of the parallelepiped having adjacent edges \(\textbf{u}, \textbf{v},\) and \(\textbf{w}\). \(\textbf{u} = \langle 0, 2, 2 \rangle\) \(\textbf{v} = \langle 0, 0, -2 \rangle\) \(\textbf{w} = \langle 3, 0, 2 \rangle\)

In Exercises 57-60, find the distance between the point and the plane. \((0, 0, 0)\) \(8x-4y+z=8\)

In Exercises 53-60, find the standard form of the equation of the sphere with the given characteristics. Center: \((-3, 7, 5);\) radius: \(10\)

In Exercises 57 and 58, write the component form of \(\textbf{v}\). \(\textbf{v}\) lies in the \(yz\)-plane, has magnitude \(4\), and makes an angle of \(45^{\circ}\) with the positive \(y\)-axis.

In Exercises 55-58, use the triple scalar product to find the volume of the parallelepiped having adjacent edges \(\textbf{u}, \textbf{v},\) and \(\textbf{w}\). \(\textbf{u} = \langle 1, 2, -1 \rangle\) \(\textbf{v} = \langle -1, 2, 2 \rangle\) \(\textbf{w} = \langle 2, 0, 1 \rangle\)

In Exercises 57 and 58, write the component form of \(\textbf{v}\). \(\textbf{v}\) lies in the \(xz\)-plane, has magnitude \(10\), and makes an angle of \(60^{\circ}\) with the positive \(z\)-axis.

In Exercises 57-60, find the distance between the point and the plane. \((3, 2, 1)\) \(x-y+2z=4\)

In Exercises 53-60, find the standard form of the equation of the sphere with the given characteristics. Center: \((0, 5, -9);\) radius: \(8\)

In Exercises 59 and 60, find the volume of the parallelepiped with the given vertices. \(A(0, 0, 0), B(4, 0, 0), C(4, -2, 3), D(0, -2, 3),\) \(E(4, 5, 3), F(0, 5, 3), G(0, 3, 6), H(4, 3, 6)\)

In Exercises 57-60, find the distance between the point and the plane. \((4, -2, -2)\) \(2x-y+z=4\)