91影视

A vector $\stackrel{\mathbf{鈫�}}{\mathbf{d}}$has a magnitude 3.0 m and is directed south. Whatare (a) the magnitude and (b) the direction of the vector$\mathbf{5}\mathbf{.}\mathbf{0}\stackrel{\mathbf{鈫�}}{\mathbf{d}}$? Whatare (c) the magnitude and (d) the direction of the vector $\mathbf{-}\mathbf{2}\mathbf{.}\mathbf{0}\stackrel{\mathbf{鈫�}}{\mathbf{d}}$?

A fire ant, searching for hot sauce in a picnic area, goes through three displacements along level ground: $\stackrel{\mathbf{鈫�}}{{\mathbf{d}}_{\mathbf{1}}}$for 0.40 msouthwest (that is, at $\mathbf{45}\mathbf{掳}$from directly south and from directly west),$\stackrel{\mathbf{鈫�}}{{\mathbf{d}}_{\mathbf{2}}}$for 0.50 mdue east,$\stackrel{\mathbf{鈫�}}{{\mathbf{d}}_{\mathbf{3}}}$for 0.60 mat$\mathbf{60}\mathbf{掳}$north of east. Let the positive x direction be east and the positive y direction be north. What are (a) the x component and (b) the y component of$\stackrel{\mathbf{鈫�}}{{\mathbf{d}}_{\mathbf{1}}}$? Next, what are (c) the x component and (d) the y component of$\stackrel{\mathbf{鈫�}}{{\mathbf{d}}_{\mathbf{2}}}$? Also, what are (e) the x component and (f) the y component of$\stackrel{\mathbf{鈫�}}{{\mathbf{d}}_{\mathbf{3}}}$?

What are (g) the x component, (h) the y component, (i) the magnitude, and (j) the direction of the ant鈥檚 net displacement? If the ant is to return directly to the starting point, (k) how far and (l) in what direction should it move?

Vector $\stackrel{\mathbf{鈫�}}{\mathbf{a}}$lies in the yz plane $\mathbf{63}\mathbf{.}\mathbf{0}\mathbf{掳}$from the positive direction of the y axis, has a positive z component, and has magnitude 3.20units. Vector $\stackrel{\mathbf{鈫�}}{\mathit{b}}$lies in xz the plane 48.0from the positive direction of the x axis, has a positive z component, and has magnitude$\mathbf{1}\mathbf{.}\mathbf{40}\mathbf{掳}$units. Find (a)role="math" localid="1661144136421" $\stackrel{\mathbf{鈫�}}{\mathbf{a}}路\stackrel{\mathbf{鈫�}}{\mathbf{b}}$, (b)$\stackrel{\mathbf{鈫�}}{\mathbf{a}}\mathbf{脳}\stackrel{\mathbf{鈫�}}{\mathbf{b}}$, and (c) the angle between$\stackrel{\mathbf{鈫�}}{\mathbf{a}}$and$\stackrel{\mathbf{鈫�}}{\mathbf{b}}$.

Find (a) 鈥渘orth cross west,鈥� (b) 鈥渄own dot south,鈥� (c) 鈥渆ast cross up,鈥� (d) 鈥渨est dot west,鈥� and (e) 鈥渟outh cross south.鈥� Let each 鈥渧ector鈥� have unit magnitude

A vector$\stackrel{\mathbf{鈬赌}}{\mathbf{B}}$, with a magnitude of$\mathbf{8}\mathbf{.}\mathbf{0}\mathbf{}\mathbf{m}$, is added to a vector $\stackrel{\mathbf{鈬赌}}{\mathbf{A}}$, which lies along an x axis. The sum of these two vectors is a third vector that lies along the y axis and has a magnitude that is twice the magnitude of$\stackrel{\mathbf{鈬赌}}{\mathbf{A}}$. What is the magnitude of $\stackrel{\mathbf{鈬赌}}{\mathbf{A}}$?

A man goes for a walk, starting from the origin of an xyz coordinate system, with the xy plane horizontal and the x axis eastward. Carrying a bad penny, he walks$\mathbf{1300}\mathbf{}\mathbf{m}$east,$\mathbf{2200}\mathbf{}\mathbf{m}$north, and then drops the penny from a cliff $\mathbf{410}\mathbf{}\mathbf{m}$high. (a) In unit-vector notation, what is the displacement of the penny from start to its landing point? (b) When the man returns to the origin, what is the magnitude of his displacement for the return trip?

A person walks in the following pattern:$\mathbf{3}\mathbf{.}\mathbf{1}\mathbf{}\mathbf{km}$north, then$\mathbf{2}\mathbf{.}\mathbf{4}\mathbf{}\mathbf{km}$west, and finallyrole="math" localid="1656154713208" $\mathbf{5}\mathbf{.}\mathbf{2}\mathbf{}\mathit{k}\mathit{m}$south. (a) Sketch the vector diagram that represents this motion. (b) How far and (c) in what direction would a bird fly in a straight line from the same starting point to the same final point?

If$\stackrel{\mathbf{鈬赌}}{\mathbf{F}}\mathbf{=}\mathit{q}\left(\stackrel{鈬赌}{v}x\stackrel{鈬赌}{B}\right)\mathbf{}\mathbf{and}\mathbf{}\stackrel{\mathbf{鈬赌}}{\mathbf{v}}$is perpendicular to$\stackrel{\mathbf{鈬赌}}{\mathbf{B}}$, then what is the direction of B in the three situations shown in Fig. 3-24 when constant q is (a) positive and (b) negative?