91Ó°ÊÓ

Write the vector, parametric and symmetric equations of the lines described. Passes through \(P=(2,1,5)\) and \(Q=(7,-2,4)\).

Find the dot product of the given vectors. \(\vec{u}=\langle 1,-1,2\rangle, \vec{v}=\langle 2,5,3\rangle\)

In Exercises 7-16, vectors \(\vec{u}\) and \(\vec{v}\) are given. Compute \(\vec{u} \times \vec{v}\) and show this is orthogonal to both \(\vec{u}\) and \(\vec{v}\). \(\vec{u}=\langle 3,2,-2\rangle, \quad \vec{v}=\langle 0,1,5\rangle\)

In Exercises 7-20, give the equation of the described plane in standard and general forms. Passes through (2,3,4) and has normal vector \(\vec{n}=\langle 3,-1,7\rangle\)

Find the dot product of the given vectors. \(\vec{u}=\langle 3,5,-1\rangle, \vec{v}=\langle 4,-1,7\rangle\)

Points \(P\) and \(Q\) are given. Write the vector \(\overrightarrow{P Q}\) in component form and using the standard unit vectors. \(P=(3,2), \quad Q=(7,-2)\)

Write the vector, parametric and symmetric equations of the lines described. Passes through \(P=(1,-2,3)\) and \(Q=(5,5,5)\).

The points \(A=(1,1,3), B=(3,2,7), C=(2,0,8)\) and \(D=(0,-1,4)\) form a quadrilateral \(A B C D\) in space. Is this a parallelogram?

Give the equation of the described plane in standard and general forms. Passes through (1,3,5) and has normal vector \(\vec{n}=\langle 0,2,4\rangle\)

Vectors \(\vec{u}\) and \(\vec{v}\) are given. Compute \(\vec{u} \times \vec{v}\) and show this is orthogonal to both \(\vec{u}\) and \(\vec{v}\). \(\vec{u}=\langle 5,-4,3\rangle, \quad \vec{v}=\langle 2,-5,1\rangle\)