Answered: Consider two vectors are in the x-y…

University Physics Volume 1

18th Edition

ISBN:9781938168277

Author:William Moebs, Samuel J. Ling, Jeff Sanny

Publisher:William Moebs, Samuel J. Ling, Jeff Sanny

Chapter2: Vectors

Section: Chapter Questions

Problem 59P: At one point in space, the direction of the electric field vector Is given In the Cartesian system...

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Consider two vectors are in the x-y plane. Vector a has a magnitude of 5.0 N and is directed along at an angle of 40 degrees from x-axis in the first quadrant, and b has magnitude of 6.0 N and is directed along at an angle of 50 degrees from y-axis in the second quadrant. Find the x and y components of vector a and vector b. Find the magnitude and direction of (vector a + vector b). Find the magnitude and direction of (vector a - vector b).

Expert Solution

Step 1

In general, a vector is defined as follows.

$\vec{A} = A_{x} \hat{i} + A_{y} \hat{j}$

Let us calculate the $x$ and $y$ components of the vector $\vec{A}$ .

$\begin{array}{rcl} A_{x} & = & A \cos θ \\ = & (5.0 N) (\cos 40 °) \\ = & 3.83 N \end{array}$

$\begin{array}{rcl} A \end{array} \begin{array}{rcl} _{y} \end{array} \begin{array}{rcl} = \end{array} \begin{array}{rcl} A \end{array} \begin{array}{rcl} \sin \end{array} \begin{array}{rcl} θ \end{array} \begin{array}{rcl} \end{array} \begin{array}{rcl} = \end{array} \begin{array}{rcl} (5.0 N) \end{array} \begin{array}{rcl} (\sin 40 °) \end{array} \begin{array}{rcl} \end{array} \begin{array}{rcl} = \end{array} \begin{array}{rcl} 3 \end{array} \begin{array}{rcl} . \end{array} \begin{array}{rcl} 21 \end{array} N$

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