91Ó°ÊÓ

Give a geometric description of the set of points in space whose coordinates satisfy the given pairs of equations. $$x=1, \quad y=0$$

Find the length and direction (when defined) of \(\mathbf{u} \times \mathbf{v}\) and \(\mathbf{v} \times \mathbf{u}.\) $$\mathbf{u}=\mathbf{i}+\mathbf{j}-\mathbf{k}, \quad \mathbf{v}=\mathbf{0}$$

Let \(\mathbf{u}=\langle 3,-2\rangle\) and \(\mathbf{v}=\langle-2,5\rangle .\) Find the \((\mathbf{a})\) component form and (b) magnitude (length) of the vector. $$\mathbf{u}-\mathbf{v}$$

Find a. \(\mathbf{v} \cdot \mathbf{u},|\mathbf{v}|,|\mathbf{u}|\) b. the cosine of the angle between \(\mathbf{v}\) and \(\mathbf{u}\) c. the scalar component of \(\mathbf{u}\) in the direction of \(\mathbf{v}\) d. the vector proj\(_\mathbf{v}\) \(\mathbf{u}\) $$\mathbf{v}=5 \mathbf{j}-3 \mathbf{k}, \quad \mathbf{u}=\mathbf{i}+\mathbf{j}+\mathbf{k}$$

Let \(\mathbf{u}=\langle 3,-2\rangle\) and \(\mathbf{v}=\langle-2,5\rangle .\) Find the \((\mathbf{a})\) component form and (b) magnitude (length) of the vector. $$2 \mathbf{u}-3 \mathbf{v}$$

Find parametric equations for the lines. The line through the origin parallel to the vector \(2 \mathbf{j}+\mathbf{k}\)

Give a geometric description of the set of points in space whose coordinates satisfy the given pairs of equations. $$x^{2}+y^{2}=4, \quad z=0$$

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

Find the length and direction (when defined) of \(\mathbf{u} \times \mathbf{v}\) and \(\mathbf{v} \times \mathbf{u}.\) $$\mathbf{u}=2 \mathbf{i}, \quad \mathbf{v}=-3 \mathbf{j}$$

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