91Ó°ÊÓ

Write the vector, parametric and symmetric equations of the lines described. Passes through \(P=(0,1,2)\) and orthogonal to both \(\vec{d}_{1}=\langle 2,-1,7\rangle\) and \(\vec{d}_{2}=\langle 7,1,3\rangle\)

Points \(P\) and \(Q\) are given. Write the vector \(\overrightarrow{P Q}\) in component form and using the standard unit vectors. \(P=(0,3,-1), \quad Q=(6,2,5)\)

Give the equation of the described plane in standard and general forms. Passes through the points (1,2,3),(3,-1,4) and (1,0,1) .

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

Find the center and radius of the sphere defined by \(x^{2}-8 x+y^{2}+2 y+z^{2}+8=0\)

Find the dot product of the given vectors. \(\vec{u}=\langle 1,2,3\rangle, \vec{v}=\langle 0,0,0\rangle\)

Points \(P\) and \(Q\) are given. Write the vector \(\overrightarrow{P Q}\) in component form and using the standard unit vectors. \(P=(2,1,2), \quad Q=(4,3,2)\)

Write the vector, parametric and symmetric equations of the lines described. Passes through \(P=(5,1,9)\) and orthogonal to both \(\vec{d}_{1}=\langle 1,0,1\rangle\) and \(\vec{d}_{2}=\langle 2,0,3\rangle\)

Find the center and radius of the sphere defined by \(x^{2}+y^{2}+z^{2}+4 x-2 y-4 z+4=0\)

Give the equation of the described plane in standard and general forms. Passes through the points (5,3,8),(6,4,9) and (3,3,3) .