Given the displacement vector , find the displacement vector so that .

Find the angles that vector makes with the and axes.

A surveyor measures the distance across a river that flows straight north by the following method. Starting directly across from a tree on the opposite bank, the surveyor walks 100 m along the river to establish a baseline. She then sights across to the tree and reads that the angle from the baseline to the tree is 35 . How wide is the river?

Suppose you walk 18.0 m straight west and then 25.0 m straight north. How far are you from your starting point? What is your displacement vector? What is the direction of your displacement? Assume the +x -axis is horizontal to the right.

If A + B = 0, the corresponding components of the two vectors Aand Bmust be (a) equal, (b) positive, (c) negative, (d) of opposite sign.

Check Your understanding Using the three displacement vectors A , B , and F in Figure 2.13, choose a convenient scale, and use a ruler and a protractor to find vector G given by the vector equation G=A+2BF . The three displacement vectors A , B , and C in Figure are specified by their magnitudes A=10.0,B=7.0 and C=8.0 , respectively, and by their respective direction angles with the horizontal direction =35,=110 , and =30 . The physical units of the magnitudes are centimeters. Choose a convenient scale and use a ruler and a protractor to find the following vector sums: (a) R=A+B , (b) D=AB , and (c) S=A3B+C .

Check Your understanding Three displacement vectors A , B , and F in (Figure 2.13) are specified by their magnitudes A=10.0,B=7.0 and F=20.00 , respectively, and by their respective direction angles with the horizontal direction =35,=110 , and =110 . The physical units of the magnitudes are centimeters. Use the analytical method to find vector G=A+2BF . Verify that G=28.15cm and that G=68.65 . The three displacement vectors A , B , and C in Figure are specified by their magnitudes A=10.0,B=7.0 and C=8.0 , respectively, and by their respective direction angles with the horizontal direction =35,=110 , and =30 . The physical units of the magnitudes are centimeters. Choose a convenient scale and use a ruler and a protractor to find the following vector sums: (a) R=A+B , (b) D=AB , and (c) S=A3B+C .

A fly enters through an open window and zooms around the room. In a Cartesian coordinate system with three axes along three edges of the room, the fly changes its position from point b(4.0m,1.5m,2.5m) to point e(1.0m,4.5in,0.5m) . Find the scalar components of the fly’s displacement vector and express its displacement vector in vector component form. What is its magnitude?

A small plane flies 40.0 km ma direction 60 north of east and then flies 30.0 km in a direction 15 north of east. Use the analytical method to find the total distance the plane covers from the starting point, and the geographic direction of its displacement vector. What is its displacement vector?