Use the component method to add the vectors and shown in Figure P3.11. Both vectors have magnitudes of and vector makes an angle of with the x axis. Express the resultant in unit-vector notation.
In a two-dimensional coordinate system, the x-component and y-component are commonly considered to be the components of a vector. It can be written as with V denoting the vector.
These are the components of vectors created along the axes. In this article, we shall find the components of any given vector using formulas for both two-dimensional and three-dimensional coordinate systems.
Discover the following components to express A in component form:
Discover the following components to express B in component form
Now find the resultant of A and B. We will add the components.
The resultant vector is
In a game of American football, a quarterback takes the ball from the line of scrimmage, runs backward a distance of 10.0 yards, and then runs sideways parallel to the line of scrimmage for 15.0 yards. At this point, he throws a forward pass downfield, 50.0 yards perpendicular to the line of scrimmage. What is the magnitude of the football's resultant displacement?
The vector has x, y, and z components of 8.00, 12.0, and 4.00 units, respectively. (a) Write a vector expression for in unit-vector notation. (b) Obtain a unit-vector expression for a vector role="math" localid="1663646691086" one-fourth the length of pointing in the same direction as . (c) Obtain a unit-vector expression for a vector role="math" localid="1663646702975" three times the length of pointing in the direction opposite the direction of .
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