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Problem 5 Easy Difficulty

5. Given the vector $\overrightarrow{A B}$ as shown, draw a vector
a. equal to $\overrightarrow{A B}$
b. opposite to $\overrightarrow{A B}$
c. whose magnitude equals $|\overrightarrow{A B}|$ but is not equal to $\overrightarrow{A B}$
d. whose magnitude is twice that of $\overrightarrow{A B}$ and in the same direction
e. whose magnitude is half that of $\overrightarrow{A B}$ and in the opposite direction

Answer

a. $\overrightarrow{A B}=\overrightarrow{C D}$
b. $\overrightarrow{A B}=-\overrightarrow{E F}$
c. $\overrightarrow{A B} \mid=\sqrt{E F}$ but $\overrightarrow{A B} \neq \overrightarrow{E F}$
d. $\overrightarrow{G H}=2 \overrightarrow{A B}$
e. $\overrightarrow{A B}=-2 \overrightarrow{J I}$

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Video Transcript

{'transcript': "We were given a vector A that points in a native boy direction, with a magnitude of five units and a vector B that has twice the magnitude of a and points of the positive X direction. Here. I've drawn Victor's A and B in red and green, respectively, Since Victor be has twice the magnitude of a vector A and Victor is five, then Victor be as a magnitude of 10. The problem wants us to find the direction and magnitude off three different combinations of these two vectors, so the 1st 1 is a plus B. A plus B will start with a intact on B. Take a listen a plus B. We also want to find a minus B. So we start with a and tack on B, but in the opposite direction, and this will be a minus B. And lastly, we want to find B minus A. So we start with B and we subtract a. This sector will be be minus a notice. How all three of these factors thes new vectors have the same magnitude, so we only have to calculate the magnitude once, and let's go ahead and calculate the magnitude for a plus B first here we can draw a right triangle such that one of the legs is 10 and the other leg is fine. So to find this magnitude h recall from Pythagorean serum we confined H as the square room of 10 squared plus five squared, which are the legs. And we get a magnitude of 11.2. This will be the magnitude for all three vectors. Now, to find the angle we have, Tanja Fader is equal too wide over acts were attention here I have labeled as this ankle always starting from the positive X axis. So here we can find data as the inverse tension of why over axe where why here is five negative five senses pointing in the native Why Direction and exits. 10. So we get an angle of negatives 26.6 degrees. This will be for a plus B. Now, for a minus being, we will have this angle as 26.6 degrees. So that will be 180 degrees plus 26.6, which equals 206.6 degrees Now for a, uh B minus A. We have theater right here, and that is just 26.6 degrees"}