91Ó°ÊÓ

Sketch the appropriate traces, and then sketch and identify the surface. $$x^{2}-y^{2}+z^{2}=1$$

Find two unit vectors orthogonal to the two given vectors. $$\mathbf{a}=\langle 1,0,4\rangle, \mathbf{b}=\langle 1,-4,2\rangle$$

Compute \(a+b, a-3 b\) and \(\|4 a+2 b\|\) $$\mathbf{a}=3 \mathbf{i}-\mathbf{j}+4 \mathbf{k}, \mathbf{b}=5 \mathbf{i}+\mathbf{j}$$

Determine whether the vectors a and b are parallel. $$\mathbf{a}=\langle-2,3\rangle, \mathbf{b}=\langle 4,6\rangle$$

State whether the lines are parallel or perpendicular and find the angle between the lines. $$\left\\{\begin{array}{l} x=1-3 t \\ y=2+4 t \\ z=-6+t \end{array} \quad \text { and } \quad\left\\{\begin{array}{l} x=1+2 s \\ y=2-2 s \\ z=-6+s \end{array}\right.\right.$$

Determine whether the vectors are orthogonal. \(\mathbf{a}=\langle 2,-1\rangle, \mathbf{b}=\langle 2,4\rangle\)

Determine whether the vectors a and b are parallel. $$\mathbf{a}=\langle 1,-2\rangle, \mathbf{b}=\langle-4,8\rangle$$

State whether the lines are parallel or perpendicular and find the angle between the lines. $$\left\\{\begin{array}{ll} x=4-2 t & \\ y=3 t & \text { and } \\ z=-1+2 t \end{array}\left\\{\begin{array}{l} x=4+s \\ y=-2 s \\ z=-1+3 s \end{array}\right.\right.$$

Sketch the appropriate traces, and then sketch and identify the surface. $$x^{2}+\frac{y^{2}}{4}-z^{2}=1$$

Find two unit vectors orthogonal to the two given vectors. $$\mathbf{a}=\langle 2,-2,1\rangle, \mathbf{b}=\langle 0,0,-2\rangle$$