91Ó°ÊÓ

In Exercises \(3-6,\) vectors \(\mathbf{A}\) and \(\mathbf{B}\) are at right angles. Find the magnitude and direction (the angle from vector \(\mathbf{A}\) ) of the resultant. \(A=14.7\) \(B=19.2\)

Vectors \(\mathbf{A}\) and \(\mathbf{B}\) are at right angles. Find the magnitude and direction (the angle from vector \(\mathbf{A}\) ) of the resultant. $$\begin{aligned} &A=3.086\\\ &B=7.143 \end{aligned}$$

Determine whether a scalar or a vector is described in (a) and (b). Explain your answers. (a) A soccer player runs 15 m from the center of the field. (b) A soccer player runs 15 m from the center of the field toward the opponents' goal.

Solve the triangles with the given parts. $$a=4.601, b=3.107, A=18.23^{\circ}$$

Solve the triangles with the given parts. $$a=63.8, B=58.4^{\circ}, C=22.2^{\circ}$$

Find the \(x\) - and \(y\) -components of the given vectors by use of the trigonometric functions. The magnitude is shown first, followed by the direction as an angle in standard position. \(76.8 \mathrm{m} / \mathrm{s}, \theta=145.0^{\circ}\)

Solve the triangles with the given parts. $$b=4384, B=47.43^{\circ}, C=64.56^{\circ}$$

Solve the triangles with the given parts. $$b=283.2, B=13.79^{\circ}, C=103.62^{\circ}$$

Draw the given vectors and find their sum graphically. The magnitude is shown first, followed by the direction as an angle in standard position. $$7.5 \mathrm{cm}, 240^{\circ} ; 2.3 \mathrm{cm}, 30^{\circ}$$

In Exercises \(15-30,\) add the given vectors by using the trigonometric functions and the Pythagorean theorem. $$\begin{aligned} &E=1653, \theta_{E}=36.37^{\circ}\\\ &F=9807, \theta_{F}=253.06^{\circ} \end{aligned}$$