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)
Accepted Solution
A:
Answer:Let [tex]\vec{A}=3\hat{i}-\hat{j}[/tex] and [tex]\vec{B}=-\hat{i}-2\hat{j}[/tex].a) [tex]\vec{A}+\vec{B}=(3\hat{i}-\hat{j})+(-\hat{i}-2\hat{j})=2\hat{i}-3\hat{j}[/tex]b) [tex]\vec{A}-\vec{B}=(3\hat{i}-\hat{j})-(-\hat{i}-2\hat{j})=4\hat{i}+\hat{j}[/tex]c) Now we calculate the direction of [tex]\vec{A}+\vec{B}[/tex] and [tex]\vec{A}-\vec{B}[/tex]We calculate the direction of [tex]\vec{A}+\vec{B}[/tex] like this:[tex]\theta=tan^{-1}(\frac{-3}{2})=-56,3^{\circ}[/tex]. Since, [tex]270\leq\theta\leq360[/tex], then the direction of [tex]\vec{A}+\vec{B}[/tex] is [tex]360^{\circ}-\theta=360^{\circ}-56.3^{\circ}=303.7^{\circ}[/tex].Now, for [tex]\vec{A}-\vec{B}[/tex][tex]\theta=tan^{-1}(\frac{1}{4})=14^{\circ}[/tex].