Review of Vectors vs. Scalars

Two perpendicular forces act on a box, one pushing to the right and one pushing up. An instrument tells you the magnitude of the total force is 13N. You measure the force pushing to the right is 12N. Calculate the force pushing up.

A delivery truck travels 8 miles in the +x-direction, 5 miles in the +y-direction, and 4 miles again in the +x-direction. What is the magnitude (in miles) of its final displacement from the origin?

Find the magnitude of the Resultant Vector D=C-B-A.

Vector F is 65 m long, directed 30.5° below the positive x-axis. (a) Find the x-component, F_x. (b) Find the y-component, F_y.

The vector A represented is by the pair of components A_x = -77 cm, A_y = 36 cm. (a) Find the magnitude of vector A. (b) Find the absolute angle of this vector.

A small helicopter travels 225 m across a city in a direction 53.1° south of east. What are the components of the helicopter’s trip?

A = (4.0 m)i + (3.0 m)j and B = (−13.0 m)i + (7.0 m)j. You add them together to produce another vector C.
(a) Express this new vector C in unit-vector notation.
(b) What are the magnitude and direction of C?

Using the vectors given in the figure, (a) find A ● B. (b) Find A ● C.

Calculate the dot product between A = (6.6 i - 3.4 j - 6.4 k ) and B = (8.6 i + 2.6 j - 5.8 k).

Find the magnitude and direction of the vector C =2B × A.