91影视

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

For any three vectors u, v and w with the same number of components,$(\mathbf{u}+\mathbf{v})+\mathbf{w}=\mathrm{\_\_\_\_\_\_\_\_\_}$

Fill in the blanks:

The distance from a point P to a plane $\mathcal{P}$containing a pointR with normal vector N is ______ .

Consider the position vector$\mathbf{i}=鉄�1,0,0鉄�$in ${\mathrm{鈩�}}^3$. Describe the set of position vectors $\mathbf{v}$in ${\mathrm{鈩�}}^3$with the property that proi,$\mathbf{v}=\mathbf{i}$.

Find the point where the line $x=鈭�7,y=t,z=5$ intersects the$xz-$plane. Explain why the line does not intersect the other two coordinate planes.

Given the equations $x=at+x_0,y=bt+y_0,z=ct+z_0$for a line $\mathfrak{L}$and $伪x+尾y+纬z=未$for a plane $蚁$explain how to determine whether $\mathfrak{L}$is orthogonal to $蚁$

Find the terminal point of a vector of magnitude \(5\) that is parallel to the vector \(\langle1,2,3\rangle\) and whose initial point is \(\left(0, 3, 鈭�2\right)\).

A function f that satisfies the hypotheses of Rolle鈥檚 Theorem on [鈭�2, 2] and for which there are exactly three values c 鈭� (鈭�2, 2) that satisfy the conclusion of the theorem .

If the triple scalar product $u路(v脳w)$ is equal to zero, what geometric relationship do the vectors u, v and w have?

Consider the function f shown in the graph next at the right. Use the graph to make a rough estimate of the average value of f on [鈭�4, 4], and illustrate this average value as a height on the graph.

If an object is moving along the graph of a vector function

$$r(t)$$ defined on an interval $$[a, b]$$, how can the distance the

object travels from $$t = a$$ to $$t = b$$ be calculated?