91Ó°ÊÓ

Find the component form of the vector. The vector \(\overrightarrow{P Q},\) where \(P=(1,3)\) and \(Q=(2,-1)\)

Match the equation with the surface it defines. Also, identify each surface by type (paraboloid, ellipsoid, etc.). The surfaces are labeled (a)-(1). $$x=z^{2}-y^{2}$$

Sketch the coordinate axes and then include the vectors \(\mathbf{u}, \mathbf{v},\) and \(\mathbf{u} \times \mathbf{v}\) as vectors starting at the origin. $$\mathbf{u}=\mathbf{i}-\mathbf{k}, \quad \mathbf{v}=\mathbf{j}$$

Find parametric equations for the lines. The line through (2,3,0) perpendicular to the vectors \(\mathbf{u}=\mathbf{i}+\) \(2 \mathbf{j}+3 \mathbf{k}\) and \(\mathbf{v}=3 \mathbf{i}+4 \mathbf{j}+5 \mathbf{k}\)

Find the component form of the vector. The vector \(\overrightarrow{O P}\) where \(O\) is the origin and \(P\) is the midpoint of segment \(R S,\) where \(R=(2,-1)\) and \(S=(-4,3)\)

Match the equation with the surface it defines. Also, identify each surface by type (paraboloid, ellipsoid, etc.). The surfaces are labeled (a)-(1). $$z=-4 x^{2}-y^{2}$$

Give a geometric description of the set of points in space whose coordinates satisfy the given pairs of equations. $$x^{2}+y^{2}+z^{2}=25, \quad y=-4$$

Find the angles between the vectors to the nearest hundredth of a radian. $$\mathbf{u}=2 \mathbf{i}-2 \mathbf{j}+\mathbf{k}, \quad \mathbf{v}=3 \mathbf{i}+4 \mathbf{k}$$

Match the equation with the surface it defines. Also, identify each surface by type (paraboloid, ellipsoid, etc.). The surfaces are labeled (a)-(1). $$x^{2}+4 z^{2}=y^{2}$$

Find the component form of the vector. The vector from the point \(A=(2,3)\) to the origin