Question

Consider the two vectors A with arrow = 3 î − ĵ and B with arrow = − î − 2 ĵ. (a) Calculate A with arrow + B with arrow 2 Correct: Your answer is correct. î + -3 Correct: Your answer is correct. ĵ (b) Calculate A with arrow − B with arrow 4 Correct: Your answer is correct. î + 1 Correct: Your answer is correct. ĵ (c) Calculate A with arrow + B with arrow (d) Calculate A with arrow − B with arrow (e) Calculate the directions of A with arrow + B with arrow and A with arrow − B with arrow. A with arrow + B with arrow Incorrect: Your answer is incorrect. Note that tan (θ + 180°) = tan θ so the inverse tangent should give two answers. Your calculator only provides one, so you must draw a careful picture of this vector to check your calculator value.° (counterclockwise from the +x axis) A with arrow − B with arrow ° (counterclockwise from the +x axis)

Answer 1

Answer:

Let $\vec{A}=3\hat{i}-\hat{j}$ and $\vec{B}=-\hat{i}-2\hat{j}$.

a)

$\vec{A}+\vec{B}=(3\hat{i}-\hat{j})+(-\hat{i}-2\hat{j})=2\hat{i}-3\hat{j}$

b)

$\vec{A}-\vec{B}=(3\hat{i}-\hat{j})-(-\hat{i}-2\hat{j})=4\hat{i}+\hat{j}$

c) Now we calculate the direction of $\vec{A}+\vec{B}$ and  $\vec{A}-\vec{B}$

We calculate the direction of $\vec{A}+\vec{B}$ like this:

$\theta=tan^{-1}(\frac{-3}{2})=-56,3^{\circ}$. Since, $270\leq\theta\leq360$, then the direction of $\vec{A}+\vec{B}$ is $360^{\circ}-\theta=360^{\circ}-56.3^{\circ}=303.7^{\circ}$.

Now, for $\vec{A}-\vec{B}$

$\theta=tan^{-1}(\frac{1}{4})=14^{\circ}$.