91影视

What point is symmetric to the point \((3, 鈭�7, 鈭�4)\) with respect to the plane \(z = 1\)?

Give an example of three nonzero vectors u, v and w in ${\mathrm{鈩�}}^3$ such that $u脳v=u脳w$ but $v鈮�w$. What geometric relationship must the three vectors have for this to happen?

Fill in the blanks:

The distance from a point P to a line $\mathrm{鈩�}$ parametrized by$\mathbf{r}\left(t\right)={\mathbf{P}}_{\mathbf{0}}+t\mathbf{d}$is ________ .

Fill in the blanks and give the name of the property.

For any two vectors u and v with the same number of components,$\mathbf{u}+\mathbf{v}=\_\_\_\_\_\_\_\_\_$

Consider the position vector $\mathbf{i}=鉄�1,0鉄�$in ${\mathrm{鈩�}}^2$. Describe the set of position vectors $\mathit{v}$in ${\mathrm{鈩�}}^2$with the property that${proj}_{\mathrm{i}}\mathbf{v}=\mathbf{i}$.

Find the points where the line $x=鈭�3t+5,y=4,z=2t+11$intersects the $xy$-plane and $yz$-plane. Explain why the line does not intersect the $xz-$plane.

The angle$胃$ between two intersecting planes called the dihedral angle is defined to be the angle between the two normal vectors to the planes, where

$胃={\cos }^{-1}\left(\frac{{\mathbf{N}}_1路{\mathbf{N}}_2}{||{\mathbf{N}}_1||||{\mathbf{N}}_2||}\right)$

Draw a figure that illustrates the dihedral angle and explain why the definition given is a reasonable definition.

What is the definition of the triple scalar product for vectors u, v and w in ${\mathrm{鈩�}}^3$?

Suppose f and g are functions such that $\underset{x鈫�3}{\lim }f\left(x\right)=5,\underset{x鈫�4}{\lim }f\left(x\right)=2$and$\underset{x鈫�3}{\lim }g\left(x\right)=4$

Given this information, calcuate the limits that follow, if possible. If it is not possible with the given information, explain why.

$\underset{x鈫�3}{\lim }-2f\left(x\right)$

Find all of the \(x, y, z\) labelings of the axes in the diagram that follows. Determine which of your labelings are right-handed systems and which are left-handed systems.